A Stochastic Differential Equation for a Class of Feller's One-dimensional Diffusion
1982; Wiley; Volume: 107; Issue: 1 Linguagem: Inglês
10.1002/mana.19821070122
ISSN1522-2616
Autores Tópico(s)Mathematical Dynamics and Fractals
ResumoA class of one-dimensional continuous strong Markovian processes is considered. Such process X were first described by William Feller in a purely analytical way, using the generalized second-order differential operator DmD. In the case of natural boundaries of the state space R and a trivial road map p(x)= x, these diffusion processes are martingales. In the present paper it is additionally assumed that the speed measure m contains a nonvanishing absolutely continous component. Then a stochastic differential equation is derived, which has the diffusion X as a weak solution.
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