A class of Lévy driven SDEs and their explicit invariant measures

2014/07/15 by Sergio Albeverio, Luca Di Persio, Albeverio, Sergio +5
Economics, Econometrics and Finance · Engineering · Mathematics · #FOS: Mathematics #Mathematical Biology Tumor Growth #Probability (math.PR) #Stability and Controllability of Differential Equations #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1407.3943

openalex publication_date 2014/07/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We describe a class of explicit invariant measures for both finite and infinite dimensional Stochastic Differential Equations (SDE) driven by Lévy noise. We first discuss in details the finite dimensional case with a linear, resp. non linear, drift. In particular, we exhibit a class of such SDEs for which the invariant measures are given in explicit form, coherently in all dimensions. We then indicate how to relate them to invariant measures for SDEs on separable Hilbert spaces.

Citations

• Foundations of Modern Probability
• Asymptotic expansions for SDE's with small multiplicative noise

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