arXiv subjects

Mingkun Ye

Publications and source records attributed to Mingkun Ye.

5 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↗

arXiv2026

Weak solution for distribution dependent SDEs driven by L\'{e}vy noise

In this paper, we establish the existence of weak solutions for distribution-dependent stochastic differential equations (DDSDEs) driven by a broad class of L\'{e}vy noises, where the drift coefficients satisfy specific integrability conditions. This is achieved through the Krylov-type estimate and tightness argument.

math.PR↗

arXiv2025

Well-Posedness and Ergodicity of Functional Stochastic Partial Differential Equations with Markovian Switching

This work focuses on a class of semi-linear functional stochastic partial differential equations with Markovian switching, in which the switching component may have finite or countably infinite states. The well-posedness of the underlying process is obtained by Skorokhod's representation of the switching component. Then, the exponential mixing of such processes in a finite state space is derived by using the so-called remote start method proposed firstly by Prato and Zabczyk in [10]. Finally, the corresponding result in a countable infinite state space is further obtained via the finite partition method.

math.PR↗

arXiv2025

Quantitative approximation to density dependent SDEs driven by $\alpha$-stable processes

Based on a class of moderately interacting particle systems, we establish a quantitative approximation for density-dependent McKean-Vlasov SDEs and the corresponding nonlinear, nonlocal PDEs. The SDE is driven by both Brownian motion and pure-jump L\'evy processes. By employing Duhamel's formula, density estimates, and appropriate martingale functional inequalities, we derive precise convergence rates for the empirical measure of particle systems toward the law of the McKean-Vlasov SDE solution. Additionally, we quantify both weak and pathwise convergence between the one-marginal particle and the solution to the McKean-Vlasov SDE. Notably, all convergence rates remain independent of the noise type.

math.PR↗

arXiv2024

The Large Deviation Principle for Stochastic Flow of Stochastic Slow-Fast Motions

In this paper, we consider a kind of fully coupled slow fast motion, in which the slow variable satisfies the non Lipschitz condition. We prove that the stochastic flow of the slow variable exists and moreover, satisfies the large deviation principle. The argument is mainly based on Khasminskii's averaging principle, the variational representation of the exponential functional of the Brownian motion, and the weak convergence framework proposed by Budhiraja and Dupuis.

math.PR↗