Ergodicity of stochastic differential equations with jumps and singular coefficients
By Longjie Xie, Xicheng Zhang. Annales De L Institut Henri Poincare-probabilites Et Statistiques, 2017
130 citations recorded by the source corpus.
We show the strong well-posedness of SDEs driven by general multiplicative Levy noises with Sobolev diffusion and jump coefficients and integrable drift. Moreover, we also study the strong Feller property, irreducibility as well as the exponential ergodicity of the corresponding semigroup when the coefficients are time-independent and singular dissipative. In particular, the large jump is allowed in the equation. To achieve our main results, we present a general approach for treating the SDEs with jumps and singular coefficients so that one just needs to focus on Krylov's {\it apriori} estimates for SDEs.
Subfields: Applied Mathematics, Finance
View Paper: https://www.semanticscholar.org/paper/3b5ef76c56404614db6ab840f97dd4eabc3eb294
How researchers see this paper
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In Applied Mathematics
- Michael Röckner
- Xicheng Zhang
- Nicolai V. Krylov
- István Gyöngy
- Franco Flandoli
- Feng-Yu Wang
- Wei Liu
- Longjie Xie
In Finance
- Michael Röckner
- Xicheng Zhang
- Wei Liu
- Nicolai V. Krylov
- István Gyöngy
- Feng-Yu Wang
- Tusheng Zhang
- Arnulf Jentzen
Citations in the corpus
- Well-posedness of distribution dependent SDEs with singular drifts (2018, background): “The following stochastic Gronwall inequality for continuous martingales was proved by Scheutzow [23], and for general discontinuous martingales in [31].”
- Existence of strong solutions for It\^o's stochastic equations via approximations. Revisited (2021, background): “, [16], [5], [24], [25], [18]) one can see that this equation has a unique strong solution.”