Stochastic Hamiltonian Type Jump Diffusion Systems with Countable Regimes: Strong Feller Property and Exponential Ergodicity

2025/09/18 by Fubao Xi, Yafei Zhai, Xi, Fubao +3
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2509.14951

openalex publication_date 2025/09/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This work focuses on a class of stochastic Hamiltonian type jump diffusion systems with state-dependent switching, in which the switching component has countably infinite many states. First,the existence and uniqueness of the underlying processes are obtained with the aid of successive construction methods. Then, the Feller property is established by coupling methods. Furthermore, the strong Feller property is proved by introducing some auxiliary processes and making use of appropriate Radon-Nikodym derivatives. Finally, on the basis of the above results, the exponential ergodicity is obtained under the Foster-Lyapunov drift condition.

Citations

• Estimating the characteristics of stochastic damping Hamiltonian systems from continuous observations
• Coupling approach for exponential ergodicity of stochastic Hamiltonian systems with Lévy noises
• On Strong Feller Property, Exponential Ergodicity and Large Deviations Principle for Stochastic Damping Hamiltonian Systems with State-Dependent Switching
• On Feller and Strong Feller Properties and Exponential Ergodicity of Regime-Switching Jump Diffusion Processes with Countable Regimes
• Approximation of Invariant Measures for Regime-Switching Diffusions
• Ergodicity of regime-switching diffusions in Wasserstein distances

Related

• On Feller and Strong Feller Properties and Exponential Ergodicity of Regime-Switching Jump Diffusion Processes with Countable Regimes
• Regime-Switching Jump Diffusions with Non-Lipschitz Coefficients and Countably Many Switching States: Existence and Uniqueness, Feller, and Strong Feller Properties
• On Strong Feller Property, Exponential Ergodicity and Large Deviations Principle for Stochastic Damping Hamiltonian Systems with State-Dependent Switching
• Strong solutions and strong Feller properties for regime-switching diffusion processes in an infinite state space
• Well-posedness and Feller property for functional stochastic Hamiltonian systems with singular coefficients and state-dependent switching