Uniqueness in law for singular degenerate SDEs with respect to a (sub-)invariant measure
We show weak existence and uniqueness in law for a general class of stochastic differential equations in \(\mathbb{R}^d\), \(d\ge 1\), with prescribed sub-invariant measure \(\widehat{\mu}\). The dispersion and drift coefficients of the stochastic differential equation are allowed to be degenerate a...
Saved in:
Published in | arXiv.org |
---|---|
Main Authors | , |
Format | Paper |
Language | English |
Published |
Ithaca
Cornell University Library, arXiv.org
23.04.2024
|
Subjects | |
Online Access | Get full text |
Cover
Loading…
Summary: | We show weak existence and uniqueness in law for a general class of stochastic differential equations in \(\mathbb{R}^d\), \(d\ge 1\), with prescribed sub-invariant measure \(\widehat{\mu}\). The dispersion and drift coefficients of the stochastic differential equation are allowed to be degenerate and discontinuous, and locally unbounded, respectively. Uniqueness in law is obtained via \(L^1(\mathbb{R}^d,\widehat{\mu})\)-uniqueness in a subclass of continuous Markov processes, namely right processes that have \(\widehat{\mu}\) as sub-invariant measure and have continuous paths for \(\widehat{\mu}\)-almost every starting point. Weak existence is obtained for a broader class via the martingale problem. |
---|---|
ISSN: | 2331-8422 |