Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Application of the dual-process method to the study of a certain singular diffusion

Author: David Williams
Journal: Trans. Amer. Math. Soc. 237 (1978), 101-110
MSC: Primary 60J35; Secondary 60H10
MathSciNet review: 0464409
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: This paper should be regarded as a sequel to a paper by Holley, Stroock and the author. Its primary purpose is to provide further illustration of the application of the dual-process method. The main result is that if $d \geqslant 2$ and $\varphi$ is the characteristic function of an aperiodic random walk on ${{\mathbf {Z}}^d}$, then there is precisely one Feller semigroup on the d-dimensional torus with generator extending $A = \{ 1 - \varphi (\theta )\} \Delta$. A necessary and sufficient condition for the associated Feller process to leave the singular point 0 is determined. This condition provides a criterion for uniqueness in law of a stochastic differential equation which is naturally associated with the process.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 60J35, 60H10

Retrieve articles in all journals with MSC: 60J35, 60H10

Additional Information

Keywords: Dual process, diffusion, Markov chain, Feller property, Bochner map, stochastic differential equation, Girsanov’s example
Article copyright: © Copyright 1978 American Mathematical Society