Explicit invariant measures for infinite dimensional SDE driven by Lévy noise with dissipative nonlinear drift I

2013/12/09 by Sergio Albeverio, Luca Di Persio, Albeverio, Sergio +5
Economics, Econometrics and Finance · Mathematics · #35C2060H15 #60651 #FOS: Mathematics #Mathematical Biology Tumor Growth #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1312.2398

openalex publication_date 2013/12/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We stu\dd y a class of nonlinear stochastic partial differential equations with dissipative nonlinear drift, driven by Lévy noise. Our work is divided in two parts. In the present part I we first define a Hilbert-Banach setting in which we can prove existence and uniqueness of solutions under general assumptions on the drift and the Lévy noise. We then prove a decomposition of the solution process in a stationary component and a component which vanishes asymptotically for large times in the L^p-sense, p≥1. The law of the stationary component is identified with the unique invariant probability measure of the process. In part II we will exhibit the invariant measure as the limit of explicit invariant measures for finite dimensional approximants.

Citations

• Foundations of Modern Probability

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