Application of the dual-process method to the study of a certain singular diffusion
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- by David Williams PDF
- Trans. Amer. Math. Soc. 237 (1978), 101-110 Request permission
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
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Additional Information
- © Copyright 1978 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 237 (1978), 101-110
- MSC: Primary 60J35; Secondary 60H10
- DOI: https://doi.org/10.1090/S0002-9947-1978-0464409-5
- MathSciNet review: 0464409