References
1986; Wiley; Linguagem: Inglês
10.1002/9780470316658.refs
ISSN1940-6347
AutoresS. N. Ethier, Thomas G. Kurtz,
Tópico(s)Markov Chains and Monte Carlo Methods
ResumoFree Access References Stewart N. Ethier, Search for more papers by this authorThomas G. Kurtz, Search for more papers by this author Book Author(s):Stewart N. Ethier, Search for more papers by this authorThomas G. Kurtz, Search for more papers by this author First published: 21 March 1986 https://doi.org/10.1002/9780470316658.refsBook Series:Wiley Series in Probability and Statistics AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onEmailFacebookTwitterLinked InRedditWechat References Abraham, Ralph and Robbin, Joel (1967). Transversal Mappings and Flows. Benjamin, New York. Google Scholar Aldous, David (1978). Stopping times and tightness. Ann. Probab. 6, 335– 340. CrossrefWeb of Science®Google Scholar Alexandron, A. D., (1940–1943). Additive set functions in abstract spaces. Mat. Sb. 8, 307– 348. Google Scholar Mat. Sb. 9, 563– 628. Google Scholar Mat. Sb. 13, 169–238. Google Scholar Allain, Marie-France (1976). Étude de la vitesse de convergence d'une suite de processus de Markov de saut pur. C. R. Acad. Set. Paris 282, 1015– 1018. Web of Science®Google Scholar Aim, Sven Erick (1978). On the rate of convergence in diffusion approximation of jump Markov processes. Technical Report, Department of Mathematics, Uppsala University, Sweden. Google Scholar Anderson, Robert F. (1976). Diffusion with second order boundary conditions, I, II. Indiana Univ. Math. J. 25, 367– 395, 403–441. CrossrefWeb of Science®Google Scholar Artstein, Zvi (1983). Distributions of random sets and random selections. Israel J. Math. 46, 313– 324. CrossrefWeb of Science®Google Scholar Athreya, Krishna B. and Ney, Peter E. (1972). Branching Processes. Springer-Verlag, Berlin. CrossrefWeb of Science®Google Scholar Barbour, Andrew D. (1974). On a functional central limit theorem for Markov population processes. Adv. Appl. Probab. 6, 21– 39. CrossrefGoogle Scholar Barbour, Andrew D. (1976). Second order limit theorems for the Markov branching process in random environments. Stochastic Process. Appl. 4, 33– 40. CrossrefGoogle Scholar Barbour, Andrew D. (1980). Equilibrium distributions for Markov population processes. Adv. Appl. Probab. 12, 591– 614. CrossrefWeb of Science®Google Scholar Bártfai, Pál (1966). Die Bestimmung des zu einem wiederkehrenden Process gehorenden Verteil-ungsfunktion aus den mil Fehlern behaften Daten eiher Einziger Relation. Stud. Sci. Math. Hung. 1, 161– 168. Google Scholar Beneŝ, Václav Edvard (1968). Finite regular invariant measures for Feller processes. J. Appl. Probab. 5, 203– 209. CrossrefWeb of Science®Google Scholar Bhattacharya, Rabi N. (1982). On the functional central limit theorem and the law of the iterated logarithm for Markov processes. Z. Wahrsch. verw. Gebiete, 60, 185– 201. CrossrefWeb of Science®Google Scholar Billingsley, Patrick (1968). Convergence of Probability Measures. Wiley, New York. Google Scholar Billingsley, Patrick (1979). Probability and Measure. Wiley, New York. Google Scholar Blackwell, David and Dubins, Lester E. (1983). An extension of Skorohod's almost sure representation theorem. Proc. Amer. Math. Soc. 89, 691– 692. Web of Science®Google Scholar Blankenship, Gilmer L. and Papanicolaou, George C. (1978). Stability and control of stochastic systems with wide band noise disturbances I. SIAM J. Appl. Math. 34, 437– 476. CrossrefWeb of Science®Google Scholar Borovkov, A. A. (1970). Theorems on the convergence to Markov diffusion processes. Z. Wahrsch. verw. Gebiete 16, 47– 76. CrossrefWeb of Science®Google Scholar Breiman, Leo (1968). Probability. Addison-Wesley, Reading, Mass. Google Scholar Brown, Bruce M. (1971). Martingale central limit theorems. Ann. Math. Statist. 42, 59– 66. CrossrefWeb of Science®Google Scholar Brown, Timothy C. (1978). A martingale approach to the Poisson convergence of simple point processes. Ann. Probab. 6, 615– 628. CrossrefPubMedGoogle Scholar Castaing, Charles (1967). Sur les multi-applications mesurables. Rev. Francaise Inf. Rech. Opéra. 1, 91– 126. Web of Science®Google Scholar Cheniov, N. N. (1956). Weak convergence of stochastic processes whose trajectories have no discontinuities of the second kind and the heuristic approach to the Kolmogorov Smirnov tests. Theory Probab. Appl. 1, 140– 149. CrossrefGoogle Scholar Chernoff, Herman (1956). Large sample theory: parametric case. Ann. Math. Statist. 27, 1– 22. CrossrefWeb of Science®Google Scholar Chernoff, Paul R. (1968). Note on product formulas for operator semigroups. J. Funct. Anal. 2, 238– 242. CrossrefGoogle Scholar Chow, Yuah Shih (1960). Martingales in a σ-finite measure space indexed by directed sets. Trans. Amer. Math. Soc. 97, 254– 285. Google Scholar Chung, Kai Lai and Williams, Ruth J. (1983). Introduction to Stochastic Integration. Birkhauser, Boston. CrossrefGoogle Scholar Cohn, Donald L. (1980). Measure Theory. Birkhauser, Boston. CrossrefGoogle Scholar Costanttni, Cristina, Gerardi, Anna and Nappo, Giovanna (1982). On the convergence of sequences of stationary jump Markov processes. Statist. Probab. Lett. 1, 155– 160. CrossrefGoogle Scholar Costantini, Cristina and Nappo, Giovanna (1982). Some results on weak convergence of jump Markov processes and their stability properties. Systems Control Lett. 2, 175– 183. CrossrefWeb of Science®Google Scholar Courrège, Philippe (1963). Integrates stochastiques et martingales de carré integrable. Séminaire Brelot-Choquet-Deny, 7th year. Google Scholar Cox, E. Theodore, and Rösier, Uwe (1982). A duality relation for entrance and exit laws for Markov processes. Stochastic Process. Appl. 16, 141– 151. CrossrefWeb of Science®Google Scholar Crandall, Michael G. and Liggett, Thomas M. (1971). Generation of semi-groups of nonlinear transformations on general Banach spaces. Amer. J. Math. 93, 265– 298. CrossrefWeb of Science®Google Scholar Csörgö, Miklós and Révész, Pál (1981). Strong Approximations in Probability and Statistics. Academic, New York. Google Scholar Darden, Thomas and Kurtz, Thomas G. (1986). Nearly deterministic Markov processes near a stable point. To appear. Google Scholar Davies, Edward Brian (1980). One-Parameter Semigroups. Academic, London. Google Scholar Davydov, Yu. A. (1968). Convergence of distributions generated by stationary stochastic processes. Theory Probab. Appl. 13, 691– 696. CrossrefWeb of Science®Google Scholar Dawson, Donald A. (1975). Stochastic evolution equations and related measure processes. J. Multivar. Anal. 5, 1– 52. CrossrefGoogle Scholar Dawson, Donald A. (1977). The critical measure diffusion process. Z. Wahrsch. verw. Gebiete 40, 125– 145. CrossrefWeb of Science®Google Scholar Dawson, Donald A. (1979). Stochastic measure diffusion processes. Canad. Math. Bull. 22, 129– 138. CrossrefGoogle Scholar Dawson, Donald A. and Hochberg, Kenneth J. (1979). The carrying dimension of a measure diffusion process. Ann. Probab. 7, 693– 703. CrossrefWeb of Science®Google Scholar Dawson, Donald A. and Kurtz, Thomas G. (1982). Applications of duality to measure-valued processes. Advances In Filtering and Optimal Stochastic Control. Lect. Notes Com. Inf. Set. 42, Springer-Verlag, Berlin, pp. 177– 191. Google Scholar Dellacherie, Claude and Meyer, Paul-André (1978). Probabilities and Potential. North-Holland, Amsterdam. Google Scholar Dellacherie, Claude and Meyer, Paul-Andre (1982). Probabilities and Potential B. North-Holland, Amsterdam. Google Scholar Doleans-Dade, Catherine (1969). Variation quadratique des martingales continues à droite. Ann. Math. Statist. 40, 284– 289. CrossrefWeb of Science®Google Scholar Doleans-Dade, Catherine and Meyer, Paul-André (1970). Intégrates stochastiques par rapport aux martingales locales. Séminalre de Probabilités IV, Lect. Notes Math., 124, Springer-Verlag, Berlin. Google Scholar Donsker, Monroe D. (1951). An invariance principle for certain probability limit theorems. Mem. Amer. Math. Soc. 6. Google Scholar Doob, Joseph L. (1953). Stochastic Processes. Wiley, New York. Web of Science®Google Scholar Dudley, Richard M. (1968). Distances of probability measures and random variables. Ann. Math. Statist. 39, 1563– 1572. CrossrefWeb of Science®Google Scholar Dunford, Nelson and Schwartz, Jacob T. (1957). Linear Operators Part I: General Theory. Wiley- Interscience, New York. Web of Science®Google Scholar Dvoretzky, Aryeh (1972). Asymptotic normality for sums of dependent random variables. Proc. Sixth Berkeley Symp. Math. Statist. Prob. 2, University of California Press, pp. 513– 535. Google Scholar Dynkin, E. B. (1961). Theory of Markov Processes. Prentice-Hall, Englewood Cliffs, N.J. Google Scholar Dynkin, E. B. (1965). Markov Processes I, II. Springer-Verlag, Berlin. CrossrefWeb of Science®Google Scholar Echeverria, Pedro E. (1982). A criterion for invariant measures of Markov processes. Z. Wahrsch. verw. Gebtete 61, 1– 16 CrossrefWeb of Science®Google Scholar Elliot, Robert J. (1982). Stochastic Calculus and Applications. Springer-Verlag, New York. Google Scholar Ethier, Stewart N. (1976). A class of degenerate diffusion processes occurring in population genetics. Comm. Pure Appt. Math. 29, 483– 493. Wiley Online LibraryWeb of Science®Google Scholar Ethier, Stewart N. (1978). Differentiability preserving properties of Markov semigroups associated with one-dimensional diffusions. Z. Wahrsch. verw. Gebiete 45, 225– 238. CrossrefWeb of Science®Google Scholar Ethier, Stewart N. (1979). Limit theorems for absorption times of genetic models. Ann. Probab. 7, 622– 738. CrossrefWeb of Science®Google Scholar Ethier, Stewart N. (1981). A class of infinite-dimensional diffusions occurring in population genetics. Indiana Univ. Math. J. 30, 925– 935. CrossrefWeb of Science®Google Scholar Ethier, Stewart N. and Kurtz, Thomas G. (1981). The infinitely-many-neutral-alleles diffusion model. Adv. Appl. Probab. 13, 429– 452. CrossrefWeb of Science®Google Scholar Ethier, Stewart N. and Kurtz, Thomas G. (1986). The infinitely-many-alleles model with selection as a measure-valued diffusion. To appear. Google Scholar Ethier, Stewart N. and Nagylaki, Thomas (1980). Diffusion approximation of Markov chains with two time scales and applications to population genetics. Adv. Appl. Probab. 12, 14– 49. Web of Science®Google Scholar Ewens, Warren J. (1972). The sampling theory of selectively neutral alleles. Theor. Pop. Biol. 3, 87– 112. CrossrefCASPubMedWeb of Science®Google Scholar Ewens, Warren J. (1979). Mathematical Population Genetics. Springer-Verlag, Berlin. Google Scholar Feller, William (1951). Diffusion processes in genetics. Proc. Second Berkeley Symp. Math. Statist. Prob., University of California Press, Berkeley, pp. 227– 246. Google Scholar Feller, William (1952). The parabolic differential equations and the associated semi-groups of transformations. Ann. Math. 55, 468– 519. CrossrefWeb of Science®Google Scholar Feller, William (1953). On the generation of unbounded semi-groups of bounded linear operators. Ann. Math. 58, 166– 174. CrossrefWeb of Science®Google Scholar Feller, William (1971). An Introduction to Probability Theory and Its Applications II, 2nd ed., Wiley, New York. Google Scholar Fiorenza, Renato (1959). Sui problemi di derivata obliqua per le equaaoni ellittiche. Ric. Mat. 8, 83– 110. Google Scholar Fisher, R. A. (1922). On the dominance ratio. Proc. Roy. Soc. Edin. 42, 321– 431. CrossrefGoogle Scholar Fleming, Wendall H. and Viot, Michel (1979). Some measure-valued Markov processes in population genetics theory. Indiana Univ. Math. J. 28, 817– 843. CrossrefWeb of Science®Google Scholar Freidlin, M. I. (1968). On the factorization of non-negative definite matrices. Theory Probab. Appl. 13, 354– 356. CrossrefWeb of Science®Google Scholar Friedman, Avner (1975). Stochastic Differential Equations I. Academic, New York. CrossrefGoogle Scholar Gänsler, Peter and Häusler, Erich (1979). Remarks on the functional central limit theorem for martingales. Z. Wahrsch. verw. Gebiete 50, 237– 243. CrossrefWeb of Science®Google Scholar Gihman, I. I. and Skorohod, A. V. (1969). Introduction to the Theory of Random Processes. W. B. Saunders Co., Philadelphia. Google Scholar Gihman, I. I. and Skorohod, A. V. (1972). Stochastic Differential Equations. Springer-Verlag, Berlin. CrossrefGoogle Scholar Gihman, I. I. and Skorohod, A. V. (1974). The Theory of Stochastic Processes I. Springer-Verlag, Berlin. CrossrefGoogle Scholar Goldstein, Jerome A. (1976). Semigroup-theoretic proofs of the central limit theorem and other theorems of analysis. Semigroup Forum 12, 189– 206. CrossrefGoogle Scholar Goldstein, Sydney (1951). On diffusion by discontinuous movements, and on the telegraph equation. Quart. J. Mech. Appl. Math. 4, 129– 156. CrossrefWeb of Science®Google Scholar Gray, Lawrence and Griffeath, David (1977a). On the uniqueness and nonuniqueness of proximity processes. Ann. Probab. 5, 678– 692. CrossrefWeb of Science®Google Scholar Gray, Lawrence and Griffeath, David (1977b). Unpublished manuscript. Google Scholar Griego, Richard J. and Hersh, Reuben (1969). Random evolutions, Markov chains, and systems of partial differential equations. Proc. Nat. Acad. Sci. USA 62, 305– 308. CrossrefCASPubMedWeb of Science®Google Scholar Griego, Richard J. and Hersh, Reuben (1971). Theory of random evolutions with applications to partial differential equations. Trans. Amer. Math. Soc. 156, 405– 418. Web of Science®Google Scholar Grigelionis, Bronius and Mikuleviĉius, R. (1981). On the weak convergence of random point processes. Lithuanian Math. Trans. 21, 49– 55. Google Scholar Grimvall, Anders (1974). On the convergence of sequences of branching processes. Ann. Probab. 2, 1027– 1045. CrossrefWeb of Science®Google Scholar Guess, Harry A. (1973). On the weak convergence of Wright-Fisher models. Stochastic Process. Appl. 1, 287– 306. CrossrefGoogle Scholar Gustafson, Karl (1966). A perturbation lemma. Bull. Amer. Math. Soc. 72, 334– 338. CrossrefWeb of Science®Google Scholar Hall, P. (1935). On representatives of subsets. J. London Math. Soc. 10, 26– 30. Wiley Online LibraryGoogle Scholar Hall, Peter and Heyde, C. C. (1980). Martingale Limit Theory and Its Applications. Academic, New York. Google Scholar Hardin, Clyde (1985). A spurious Brownian motion. Proc. Amer. Math. Soc. 93, 350. CrossrefWeb of Science®Google Scholar Harris, Theodore E. (1976). On a class of set-valued Markov processes. Ann. Probab. 4, 175– 194. CrossrefWeb of Science®Google Scholar Hasegawa, Minoru (1964). A note on (he convergence of semi-groups of operators. Proc. Japan Acad. 40, 262– 266. CrossrefGoogle Scholar Helland, Inge S. (1978). Continuity of a class of random time transformations. Stochastic Process. Appl. 7, 79– 99. CrossrefGoogle Scholar Helland, Inge S. (1981). Minimal conditions for weak convergence to a diffusion process on the line. Ann. Probab. 9, 429– 452. CrossrefWeb of Science®Google Scholar Helland, Inge S. (1982). Central limit theorems for martingales with discrete or continuous time. Scand. J. Statist. 9, 79– 94. Web of Science®Google Scholar Helms, Lester L. (1974). Ergodic properties of several interacting Poisson particles. Adv. Math. 12, 32– 57. CrossrefWeb of Science®Google Scholar Hersh, Reuben (1974). Random evolutions: a survey of results and problems. Rocky Mt. J. Math. 4, 443– 477. CrossrefGoogle Scholar Hersh, Reuben and Papanicolaou, George C. (1972). Non-commuting random evolutions, and an operator-valued Feynman-Kac formula. Comm. Pure Appl. Math. 25, 337– 367. Wiley Online LibraryWeb of Science®Google Scholar Heyde, C. C. (1974). On the central limit theorem for stationary processes. Z. Wahrsch. verw. Gebietc 30, 315– 320. CrossrefWeb of Science®Google Scholar Hille, Einar (1948). Functional Analysis and Semi-groups, Am. Math. Soc Colloq. Publ. 31, New York. Google Scholar Hille, Einar and Phillips, Ralph (1957). Functional Analysis and Semi-groups, rev. ed., Amer. Math. Soc. Colloq. Publ. 31, Providence, R.I. Google Scholar Himmelberg, C J. (1975). Measurable relations. Fund. Math. 87, 53– 72. CrossrefGoogle Scholar Holley, Richard A. and Liggett, Thomas M. (1975). Ergodic theorems for weakly interacting systems and the voter model. Ann. Probab. 3, 643– 663. CrossrefWeb of Science®Google Scholar Holley, Richard A. and Stroock, Daniel W. (1976). A martingale approach to infinite systems of interacting processes. Ann. Probab. 4, 195– 228. CrossrefWeb of Science®Google Scholar Holley, Richard A. and Stroock, Daniel W. (1978). Generalized Ornstein-Uhlenbeck processes and infinite particle branching Brownian motions. Publ. RIMS, Kyoto Univ. 14, 741– 788. CrossrefGoogle Scholar Holley, Richard A. and Stroock, Daniel W. (1979). Dual processes and their applications to infinite interacting systems. Adv. Math. 32, 149– 174. CrossrefWeb of Science®Google Scholar Holley, Richard A., Stroock, Daniel W., and Williams, David (1977). Applications of dual processes to diffusion theory. Proc. Symp. Pure Math. 31, AMS, Providence, R.I., pp. 23– 36. Google Scholar Ibragimov, I. A. (1959). Some limit theorems for strict-sense stationary stochastic processes. Dokl. Akad. Nauk SSSR, 125, 711– 714. Web of Science®Google Scholar Ibragimov, I. A. (1962). Some limit theorems for stationary processes. Theory Probab. Appl. 7, 349– 382. CrossrefGoogle Scholar Ibragimov, I. A. and Linnik, Yu. V. (1971). Independent and Stationary Sequences of Random Variables. Wolters-Noordhoff, Groningen. Google Scholar Ikeda, Nobuyuki, Nagasawa, Masao, and Watanabe, Shinzo (1968, 1969). Branching Markov processes I, II, III. J. Math. Kyoto 8, 233– 278, 365–410. Google Scholar J. Math. Kyoto 9, 95– 160. Google Scholar Ikeda, Nobuyuki and Watanabe, Shinzo (1981). Stochastic Differential Equations and Diffusion Processes. North Holland, Amsterdam. Google Scholar Il'in, A. M., Kalashnikov, A. S., and Oleinik, O. A. (1962). Linear equations of the second order of parabolic type. Russ. Math. Surveys 17, 1– 143. CrossrefGoogle Scholar Itǒ, Kiyosi (1951). On stochastic differential equations. Mem. Amer. Math. Soc. 4. Google Scholar Itǒ, Kiyosi and Watanabe, Shinzo (1965). Transformations of Markov processes by multiplicative functionals. Ann. Inst. Fourier 15, 15– 30. Google Scholar Jacod, Jean, Memin, Jean, and Métivier, Michel (1983). On tightness and stopping times. Stochastic Process. Appl. 14, 109– 146. CrossrefGoogle Scholar Sagera, Peter (1971). Diffusion approximations of branching processes. Ann. Math. Statist. 42, 2074– 2078. CrossrefWeb of Science®Google Scholar Jifina, Miloslav (1969). On Feller's branching diffusion processes. Ĉasopis Pèst. Mat. 94, 84– 90. Google Scholar Joffe, Anatole and Metivier, Michel (1984). Weak convergence of sequences of semimartingales with applications to multitype branching processes. Tech. Rep., Université de Montréal. Google Scholar Kabanov, Yu. M., Lipster, R. Sh., and Shiryaev, A. N. (1980). Some limit theorems for simple point processes (a martingale approach). Stochastics 3, 203– 216. CrossrefGoogle Scholar Kac, Mark (1956). Some stochastic problems in physics and mathematics. Magnolia Petroleum Co. Colloq. Lect. 2. Google Scholar Kac, Mark (1974). A stochastic model related to the telegrapher's equation. Rocky Mi. J. Math., 4, 497– 509. CrossrefGoogle Scholar Kallman, Robert R. and Rota, Gian-Carlo (1970). On the inequality ‖f‖2≤4‖f‖·‖f‖. Inequalities, Vol. II, Oved Shisha, Ed. Academic, New York, pp. 187– 192. Google Scholar Karlin, Samuel and Levikson, Benny (1974). Temporal fluctuations in selection intensities: Case of small population size. Theor. Pop. Biol. 6, 383– 412. CrossrefWeb of Science®Google Scholar Kato, Tosio (1966). Perturbation Theory for Linear Operators. Springer-Verlag, New York. CrossrefGoogle Scholar Keiding, Niels (1975). Extinction and exponential growth in random environments. Theor. Pop. Biol. 8, 49– 63. CrossrefPubMedWeb of Science®Google Scholar Kertz, Robert P. (1974). Perturbed semigroup limit theorems with applications to discontinuous random evolutions. Trans. Amer. Math. Soc. 199, 29– 53. CrossrefWeb of Science®Google Scholar Kertz, Robert P. (1978). Limit theorems for semigroups with perturbed generators, with applications to multiscaled random evolutions. J. Fund. Anal. 27, 215– 233. CrossrefWeb of Science®Google Scholar Khas'minskii, R. Z. (1960). Ergodic properties of recurrent diffusion processes and stabilization of the solution of the Cauchy problem for parabolic equations. Theory Probab. Appl. 5, 179– 196. CrossrefGoogle Scholar Khas'minskii, R. Z. (1966). A limit theorem for the solutions of differential equations with random right-hand sides. Theory Probab. Appl. 11, 390– 406. CrossrefWeb of Science®Google Scholar Khas'minskii, R. Z. (1980). Stochastic Stability of Differential Equations. Sijthoff and Nordhoff. Google Scholar Khintchine, A. (1933). Asymptotische Gesetze der Wahrscheinlichkeitsrechnunq. Springer-Verlag, Berlin. CrossrefGoogle Scholar Kimura, Motoo and Crow, James F. (1964). The number of alleles that can be maintained in a finite population. Genetics 49, 725– 738. CrossrefCASPubMedWeb of Science®Google Scholar Kingman, J. F. C. (1967). Completely random measures. Pacific J. Math. 21, 59– 78. CrossrefWeb of Science®Google Scholar Kingman, J. F. C. (1975). Random discrete distributions. J. R. Statist. Soc. B 37, 1– 22. Wiley Online LibraryWeb of Science®Google Scholar Kingman, J. F. C. (1977). The population structure associated with the Ewens sampling formula. Theor. Pop. Biol. 11, 274– 283. CrossrefCASPubMedWeb of Science®Google Scholar Kingman, J. F. C. (1980). Mathematics of Genetic Diversity. CBMS-NSF Regional Conf. Series in Appl. Math., 34, SIAM, Philadelphia. CrossrefGoogle Scholar Kolmogorov, A. N. (1956). On Skorohod convergence. Theory Probab. Appl. 1, 213– 222. CrossrefGoogle Scholar Komlós, János, Major, Peter, and Tusnády, Gábor (1975, 1976). An approximation of partial sums of independent RV's and the sample DF I, II. Z. Wahrsch. verw. Gebiete 32, 111– 131. CrossrefWeb of Science®Google Scholar Z. Wahrsch. verw. Gebiete 34, 33– 58. Google Scholar Krylov, N. V. (1973). The selection of a Markov process from a system of processes and the construction of quasi-diffusion processes. Math. USSR Izoestia 7, 691– 709. CrossrefGoogle Scholar Kunita, Hiroshi and Watanabe, Shinzo (1967). On square integrable martingales. Naqoya Math. J. 30, 209– 245. CrossrefWeb of Science®Google Scholar Kuratowski, K. and Ryll-Nardzewski, C. (1965). A general theorem on selectors. Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 13, 397– 403. Web of Science®Google Scholar Kurtz, Thomas G. (1969). Extensions of Trotter's operator semigroup approximation theorems. J. Funct. Anal. 3, 354– 375. CrossrefGoogle Scholar Kurtz, Thomas G. (1970a). A general theorem on the convergence of operator semigroups. Trans. Amer. Math. Soc. 148, 23– 32. CrossrefWeb of Science®Google Scholar Kurtz, Thomas G. (1970b). Solutions of ordinary differential equations as limits of pure jump Markov processes. J. Appl. Probab. 7, 49– 58. Web of Science®Google Scholar Kurtz, Thomas G. (1971). Limit theorems for sequences of jump Markov processes approximating ordinary differential processes. J. Appl. Probab. 8, 344– 356. CrossrefWeb of Science®Google Scholar Kurtz, Thomas G. (1973). A limit theorem for perturbed operator semigroups with applications to random evolutions. J. Funct. Anal. 12, 55– 67. CrossrefGoogle Scholar Kurtz, Thomas G. (1975). Semigroups of conditioned shifts and approximation of Markov processes. Ann. Probab. 3, 618– 642. CrossrefWeb of Science®Google Scholar Kurtz, Thomas G. (1977). Applications of an abstract perturbation theorem to ordinary differential equations. Houston J. Math. 3, 67– 82. Google Scholar Kurtz, Thomas G. (1978a). Strong approximation theorems for density dependent Markov chains. Stochastic Process. Appl. 6, 223– 240. CrossrefGoogle Scholar Kurtz, Thomas G. (1978b). Diffusion approximations for branching processes. Branching Processes, Adv. Prob. 5, Anatole Joffe, and Peter Ney, Eds., Marcel Dekker, New York, pp. 262– 292. Google Scholar Kurtz, Thomas G. (1980a). Representation of Markov processes as multiparameter time changes. Ann. Probab. 8, 682– 715. CrossrefWeb of Science®Google Scholar Kurtz, Thomas G. (1980b). The optional sampling theorem for martingales indexed by directed sets. Ann. Probab. 8, 675– 681. CrossrefWeb of Science®Google Scholar Kurtz, Thomas G. (1981a). Approximation of Population Processes. CBMS-NSF Regional Conf. Series in Appl. Math. 36, SIAM, Philadelphia. CrossrefGoogle Scholar Kurtz, Thomas G. (1981b). The central limit theorem for Markov chains. Ann. Probab. 9, 557– 560. CrossrefWeb of Science®Google Scholar Kurtz, Thomas G. (1981c). Approximation of discontinuous processes by continuous processes. Stochastic Nonlinear Systems, L. Arnold, and R. Lefever, Eds. Springer-Verlag, Berlin, pp. 22– 35. Google Scholar Kurtz, Thomas G. (1982). Representation and approximation of counting processes. Advances in Filtering and Optimal Stochastic Control, Led. Notes Com. Inf. Sci. 42, W. H. Fleming and L. G. Gorostiza, Eds., Springer-Verlag, Berlin. Google Scholar Kushner, Harold J. (1974). On the weak convergence of interpolated Markov chains to a diffusion. Ann. Probab. 2, 40– 50. CrossrefWeb of Science®Google Scholar Kushner, Harold J. (1979). Jump-diffusion approximation for ordinary differential equations with wide-band random right hand sides. SIAM J. Control Optim. 17, 729– 744. CrossrefWeb of Science®Google Scholar Kushner, Harold J. (1980). A martingale method for the convergence of a sequence of processes to a jump-diffusion process on the line. Z. Wahrsch. verw. Geblete 53, 207– 219. CrossrefWeb of Science®Google Scholar Kushner, Harold J. (1982). Asymptotic distributions of solutions of ordinary differential equations with wide band noise inputs; approximate invariant measures. Stochastics 6, 259– 277. CrossrefGoogle Scholar Kushner, Harold J. (1984). Approximation and Weak Convergence Methods for Random Processes. MIT Press, Cambridge, Massachusetts. Google Scholar Ladyzhenskaya, O. A. and Ural'tseva, N. N. (1968). Linear and Quasilinear Elliptic Partial Differential Equations. Academic, New York. Google Scholar Lampeni, John (1967a). The limit of a sequence of branching processes. Z. Wahrsch. ve
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