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Guangjun Shen

Publications and source records attributed to Guangjun Shen.

7 recordsLinked to original sources
arXiv2026

Almost sure exponential stability of multi-dimensional stochastic systems driven by a symmetric $α$-stable process

This article investigates the stability of a class of multidimensional stochastic systems driven by a symmetric $α$-stable process with $1<α<2$. These driving processes have infinite second moments, which prevents the direct application of standard second-moment methods and may lead to divergent jump integrals in the generators of quadratic Lyapunov functions. We establish criteria for $p$th-moment exponential stability and almost sure exponential stability. A numerical example illustrates the theoretical results.

math.PR↗
arXiv2025

Euler-Maruyama method for distribution dependent stochastic differential equation driven by multiplicative fractional Brownian motion

In this paper, we establish the propagation of chaos and Euler-Maruyama method of DDSDE driven by multiplicative fractional Brownian motion with Hurst parameter $H\in (\frac{\sqrt{5}-1}{2},1)$. We have not only obtained an upper bound for the error of the Euler-Maruyama method but also verified the correctness of this result via systematic numerical simulation experiments.

math.PR↗
arXiv2023

Stochastic averaging principle and stability for multi-valued McKean-Vlasov stochastic differential equations with jumps

In this paper, we consider the stochastic averaging principle and stability for multi-valued McKean-Vlasov stochastic differential equations with jumps. First, under certain averaging conditions, we are able to show that the solutions of the equations concerned can be approximated by solutions of the associated averaged multi-valued McKean-Vlasov stochastic differential equations with jumps in the sense of the mean square convergence. Second, we extend the classical Itô's formula from stochastic differential equations to multi-valued McKean-Vlasov stochastic differential equations with jumps. Last, as application of Itô's formula, we present the exponential stability of second moments, the exponentially 2-ultimate boundedness and the almost surely asymptotic stability for their solutions in terms of a Lyapunov function.

math.PR↗
arXiv2018

Limit theorems for functionals of Gaussian vectors

Operator self-similar processes, as an extension of self-similar processes, have been studied extensively. In this work, we study limit theorems for functionals of Gaussian vectors. Under some conditions, we determine that the limit of partial sums of functionals of a stationary Gaussian sequence of random vectors is an operator self-similar process

math.PR↗
arXiv2018

Operator Fractional Brownian Sheet and Martingale Differences

In this paper, inspired by the fractional Brownian sheet of Riemann-Liouville type, we introduce the operator fractional Brownian sheet of Riemman-Liouville type, and study some properties of it. We also present an approximation in law to it based on the martingale differences.

math.PR↗
arXiv2015

An optimal approximation of Rosenblatt sheet by multiple Wiener integrals

Let $Z^{α,β}$ be the Rosenblatt sheet with the representation $$ Z^{α,β}(t,s)=\int^t_0\int^s_0\int^t_0\int^s_0Q^α(t,y_1,y_2)Q^β(s,u_1,u_2)B(dy_1,du_1)B(dy_2,du_2) $$ where $B$ is a Brownian sheet, $\frac12<α,β<1$, $Q^α$ and $Q^β$ are the given kernel. In this paper, we contruct multiple Wiener integrals of the form \begin{align*} \int^t_0\int^s_0\int^t_0\int^s_0&[k_1(y_1,y_2)^{-\frac12α}(u_1,u_2)^{-\frac12β}+k_2(y_1\vee y_2)^{\frac12α}(y_1\wedge y_2)^{-\frac12α}|y_1-y_2|^{α-1}\\ &\cdot(u_1\vee u_2)^{\frac12β}(u_1\wedge u_2)^{-\frac12β}|u_1-u_2|^{β-1}]B(dy_1,du_1)B(dy_2,du_2),~~k_1,k_2\geq0, \end{align*} and obtain an optimal approximation of $Z^{α,β}(t,s)$.

math.PR↗