Large deviations for invariant measures of stochastic differential equations with jumps. Issue 4 (19th May 2019)

• Record Type: Journal Article
• Authors: Ma, Xiaocui; Xi, Fubao
• Is Part Of: Stochastics. Volume 91:Issue 4(2019)
• Page Start: 528
• Page End: 552
• Publication Date: 2019-05-19
• Subjects: Large deviation -- invariant measure -- strong Feller property -- irreducibility -- Poisson random measure; 60F60 -- 60H10 -- 60A10; Stochastic processes -- Periodicals; Probabilities -- Periodicals; 519.2
• DOI: 10.1080/17442508.2018.1557184
• Languages: English
• ISSNs: 1744-2508

Abstract

ABSTRACT: Large deviation principle (LDP) for the invariant measures of stochastic differential equations with jumps is obtained. First, we prove{ X ε ( t ) } ε > 0 given as the solutions of the stochastic differential equations have invariant measures{ μ ε ( ⋅ ) } ε > 0 . In order to ensure the uniqueness of the invariant measures, the strong Feller property and irreducibility for the Markov semigroup are proved. Moreover, the LDP for the invariant measures{ μ ε ( ⋅ ) } ε > 0 is established. The proof of the LDP forμ ε is based on the LDP for{ X ε ( t ) } ε > 0, which have been studied by Budhiraja et al. [5].