Jump-diffusions with state-dependent switching: existence and uniqueness, Feller property, linearization, and uniform ergodicity
type: Item
instance of: scholarly article
title: Jump-diffusions with state-dependent switching: existence and uniqueness, Feller property, linearization, and uniform ergodicity
zbMATH Open document ID: 1274.60253
author: Gang Yin
author: Fubao Xi
published in: Science China. Mathematics
publication date: 2013-01-29T00:00:00Z
review text: The authors analyze a class of jump-diffusions with state-space dependent switching. In contrast to previous work their model allows for a characteristic measure which is \(\sigma\)-finite. `Existence and uniqueness of the underlying process are obtained by representing the switching component as a stochastic integral with respect to a Poisson random measure and by using a successive approximation method'. Furthermore the authors prove the Feller property. To this end they introduce auxiliary processes and they make use of Radon-Nikodym derivatives. Irreducibility and the fact that `all compact sets being petite are demonstrated. Based on these results, the uniform ergodicity is established under a general Lyapunov condition. Finally, easily verifiable conditions for uniform ergodicity are established when the jump-diffusions are linearizable with respect to the variable \(x\) (the state variable corresponding to the jump-diffusion component) in a neighborhood of the infinity'. The results are illustrated by some examples.
reviewed by: Alexander Schnurr
Mathematics Subject Classification ID: 60J75
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 60J60
Mathematics Subject Classification ID: 60J27
zbMATH DE Number: 6132163
zbMATH Keywords: jump-diffusion
zbMATH Keywords: sigma-finite characteristic measure
zbMATH Keywords: state-dependent switching
zbMATH Keywords: Feller property
zbMATH Keywords: Poisson random measure
zbMATH Keywords: uniform ergodicity
zbMATH Keywords: linearization
MaRDI profile type: Publication
full work available at URL: s11425-011-4281-y
OpenAlex ID: W2260817477
cites work: Stability of degenerate diffusions with state-dependent switching
cites work: Q4650356
cites work: Exponential and uniform ergodicity of Markov processes
cites work: Ergodic Control of Switching Diffusions
cites work: Linear diffusion with stationary switching regime
cites work: Q3959169
cites work: Stability of regime-switching diffusions
cites work: Q4197143
cites work: Almost sure stability of linear stochastic differential equations with jumps
cites work: Stability of stochastic differential equations with Markovian switching
cites work: Stability of Markovian processes I: criteria for discrete-time Chains
cites work: Stability of Markovian processes II: continuous-time processes and sampled chains
cites work: Stability of Markovian processes III: Foster–Lyapunov criteria for continuous-time processes
cites work: Criteria for ergodicity of Lévy type operators in dimension one
cites work: Regularity of semigroups generated by Lévy type operators via coupling
cites work: Stability for multidimensional jump-diffusion processes
cites work: Asymptotic properties of jump-diffusion processes with state-dependent switching
cites work: Asymptotic Properties of a Mean-Field Model with a Continuous-State-Dependent Switching Process
cites work: On the stability of diffusion processes with state-dependent switching
cites work: Stability of Regime-Switching Jump Diffusions
cites work: Hybrid switching diffusions. Properties and applications
cites work: Asymptotic stability in distribution of stochastic differential equations with Markovian switching.
cites work: Asymptotic Properties of Hybrid Diffusion Systems
DOI: 10.1007/S11425-011-4281-Y
description: scientific article; zbMATH DE number 6132163