Stochastic delay differential equations with jump reflection: invariant measure. Issue 6 (17th August 2016)

• Record Type: Journal Article
• Authors: Bo, Lijun; Yuan, Chenggui
• Is Part Of: Stochastics. Volume 88:Issue 6(2016)
• Page Start: 841
• Page End: 863
• Publication Date: 2016-08-17
• Subjects: Stochastic delay differential equations -- jump reflection -- invariant measure -- local time; 60J60 -- 60K10; Stochastic processes -- Periodicals; Probabilities -- Periodicals; 519.2
• DOI: 10.1080/17442508.2016.1149589
• Languages: English
• ISSNs: 1744-2508

Abstract

Abstract : In this paper, we consider a class of multi-dimensional stochastic delay differential equations with jump reflection. Based on existence and uniqueness of the strong solution to equation, we prove that the Markov semigroup generated by the segment process corresponding to the solution admits a unique invariant measure on the Skorohod space when the coefficients of equation satisfy a class of monotone conditions. Finally, we establish a relationship between the regulator and the local time of the solution and discuss a local time property at large time under the stationary setting.