5 papers · 1 filter
Generalized Ornstein-Uhlenbeck process for affine stochastic functional differential equations and its applications
Xiang Lv
This paper studies the existence and global stability of generalized Ornstein-Uhlenbeck process for affine stochastic functional differential equations. Various very basic and impo…
An abstract criterion on the existence and global stability of stationary solutions for random dynamical systems and its applications
Xiang Lv
We prove a concise and easily verifiable criterion on the existence and global stability of stationary solutions for random dynamical systems (RDSs). As a consequence, we can show…
Small-gain theorems for nonlinear stochastic systems with inputs and outputs II: Multiplicative white noise case
Jifa Jiang, Xiang Lv
This paper is a continuation of the paper \cite{JL}, which focuses on exploring the global stability of nonlinear stochastic feedback systems on the nonnegative orthant driven by m…
A small-gain theorem for nonlinear stochastic systems with inputs and outputs I: Additive white noise
Jifa Jiang, Xiang Lv
This paper studies a small-gain theorem for nonlinear stochastic equations driven by additive white noise in both trajectories and stationary distribution. Motivated by the most re…
Infinitely many homoclinic solutions for a class of subquadratic second-order Hamiltonian systems
Xiang Lv
In this paper, we mainly consider the existence of infinitely many homoclinic solutions for a class of subquadratic second-order Hamiltonian systems , wh…