Stability for multidimensional jump-diffusion processes
type: Item
instance of: scholarly article
title: Stability for multidimensional jump-diffusion processes
zbMATH Open document ID: 0962.60046
DOI: 10.1016/S0304-4149(98)00078-7
author: In-Suk Wee
published in: Stochastic Processes and their Applications
publication date: 2001-01-17T00:00:00Z
review text: Consider an \(n\)-dimensional jump-diffusion process \(\{X^x_t\}\) satisfying \[ X^x_t=x+\int _0^t\mu (X^x_{s-}) ds + \int _0^t\sigma (X^x_{s-}) dB_s + \int _0^t \int c(X^x_{s-},u)\widetilde \nu (ds,du), \] where \(\mu (x)\) and \(c(x,u)\) are \(R^n\)-valued and \(\sigma (x)\) is \(n\times m\)-matrix valued for \(x,u\in R^n\), \(\{B_t\}\) denotes a standard \(m\)-dimensional Brownian motion and \(\widetilde \nu (ds,dy)\) a compensated Poisson random measure. Sufficient conditions for existence and uniqueness of an invariant measure, for stability in distribution of solutions, for stochastic stability, stochastic asymptotic stability and a.s. exponential stability of an equilibrium solution are given.
Mathematics Subject Classification ID: 60H10
zbMATH DE Number: 1554298
zbMATH Keywords: jump-diffusion process
zbMATH Keywords: stochastic stability
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1554298