arXiv subjects

Yafei Zhai

Publications and source records attributed to Yafei Zhai.

4 recordsLinked to original sources

arXiv2026

Ergodicity of stochastic functional differential equation with jumps and finite delay

This paper investigates the ergodicity of stochastic functional differential equations with jumps under the Wasserstein distance by the generalized coupling method. Two key conditions are verified. The first is verified by establishing an exponential decay bound for the coupled segment processes and applying the Girsanov theorem for It\^o-L\'evy processes. The second is verified through a support theorem developed for an auxiliary process and then extended to the underlying process. Combining these results yields the desired ergodicity.

math.PR↗

arXiv2025

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

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.

math.PR↗

arXiv2025

Well-posedness and Feller property for functional stochastic Hamiltonian systems with singular coefficients and state-dependent switching

This work focuses on a class of functional stochastic Hamiltonian systems with singular coefficients and state-dependent switching, in which the switching process has a countably infinite state space. First, by Girsanov's transformation, we establish the martingale solution of the system in each fixed switching case. Then, since the two components of the system are intertwined and correlated, we investigate the special case when the discrete component is independent of the continuous component. Based on these results, we obtain the well-posedness of the system with the aid of a martingale process. Finally, in order to establish the Feller property, we take advantage of appropriate Radon-Nikodym derivative and introduce a vector valued elliptic equation to handle the effect of the singular coefficients.

math.PR↗

arXiv2025

Switching Diffusion Systems with Past-Dependent Switching and Countable State Space: Successful Couplings and Strong Ergodicity

This work studies a class of switching diffusion systems where the switching component takes values in a countable state space and its transition rates depend on the history of the continuous component. Under suitable conditions, we construct a successful coupling that establishes stability of the underlying process in the total variation norm. The coupling approach also enables us to derive strong ergodicity for the underlying process. Finally, we illustrate the main results with an $N$-body mean-field model featuring past-dependent switching and a countable state space.

math.PR↗