On Absolute Continuity of Feller's One-Dimensional Diffusion Processes
1984; Wiley; Volume: 116; Issue: 1 Linguagem: Inglês
10.1002/mana.19841160122
ISSN1522-2616
Autores Tópico(s)Stochastic processes and statistical mechanics
ResumoA class of FELLER's one-dimemsional continuous strong MARKOV processes generated by the generalized second order differential operator DmD8+ is considered. In the case of natural boundaries of the state space ℜ︁ and an identical road map s(x) = x, these diffusion processes are martingales. In a first part of this note some earlier results concerning the representation of such processes as weak solutions of stochastic differential equations are improved. The second part concerns with diffusions absolutely continuous with respect to a given one, determined by the generator DmD. Such absolutely continuous diffusions on the line were first described analytically by S. OREY in terms of the corresponding speed measures and road maps. By the aid of the derived stochastic equations an explicit expression for the corresponding RADON-NIKODYM derivatives is possible. This allows a characterization of diffusions with non-identical scale functions by stochastic differential equations.
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