13 papers
Random attractors and almost-sure stability under discretization of a stochastic autoparametric system
Chuchu Chen, Jialin Hong, Yibo Wang
For a stochastic autoparametric block-and-pendulum system, the long-time dynamics exhibit two fundamental features: the almost-sure stability of the single mode solution, character…
Symplectic methods for stochastic Hamiltonian systems: asymptotic error distributions and Hamiltonian-specific analysis
Chuchu Chen, Xinyu Chen, Jialin Hong +1
In this paper, we investigate the asymptotic error distributions of symplectic methods for stochastic Hamiltonian systems and further provide Hamiltonian-specific analysis that cla…
The law of iterated logarithm for numerical approximation of time-homogeneous Markov process
Chuchu Chen, Xinyu Chen, Jialin Hong
The law of the iterated logarithm (LIL) for the time-homogeneous Markov process with a unique invariant measure characterizes the almost sure maximum possible fluctuation of time a…
Random attractor and SRB measure for stochastic Hopf bifurcation under discretization
Chuchu Chen, Jialin Hong, Yibo Wang
Chaotic phases in stochastic differential equations are characterized by two essential long-time dynamical features: a random attractor capturing asymptotic geometry and a Sinai-Ru…
-strong convergence orders of fully discrete schemes for the SPDE driven by Lévy noise
Chuchu Chen, Tonghe Dang, Jialin Hong +1
It is well known that for a stochastic differential equation driven by Lévy noise, the temporal Hölder continuity in sense of the exact solution does not exceed . This l…
A new class of splitting methods that preserve ergodicity and exponential integrability for stochastic Langevin equation
Chuchu Chen, Tonghe Dang, Jialin Hong +1
In this paper, we propose a new class of splitting methods to solve the stochastic Langevin equation, which can simultaneously preserve the ergodicity and exponential integrability…
On structure preservation for fully discrete finite difference schemes of stochastic heat equation with Lévy space-time white noise
Chuchu Chen, Tonghe Dang, Jialin Hong
This paper investigates the structure preservation and convergence analysis of a class of fully discrete finite difference schemes for the stochastic heat equation driven by Lévy s…
Superiority of stochastic symplectic methods via the law of iterated logarithm
Chuchu Chen, Xinyu Chen, Tonghe Dang +1
The superiority of stochastic symplectic methods over non-symplectic counterparts has been verified by plenty of numerical experiments, especially in capturing the asymptotic behav…
Longtime behaviors of -Euler-Maruyama method for stochastic functional differential equations
Chuchu Chen, Tonghe Dang, Jialin Hong +1
This paper investigates longtime behaviors of the -Euler-Maruyama method for the stochastic functional differential equation with superlinearly growing coefficients. We focus on…
Long-time weak convergence analysis of a semi-discrete scheme for stochastic Maxwell equations
Chuchu Chen, Jialin Hong, Ge Liang
It is known from the monograph [1, Chapter 5] that the weak convergence analysis of numerical schemes for stochastic Maxwell equations is an unsolved problem. This paper aims to fi…
Long-time dynamics of stochastic wave equation with dissipative damping and its full discretization: exponential ergodicity and strong law of large numbers
Meng Cai, Chuchu Chen, Jialin Hong +1
For stochastic wave equation, when the dissipative damping is a non-globally Lipschitz function of the velocity, there are few results on the long-time dynamics, in particular, the…
Probabilistic limit behaviors of numerical discretizations for time-homogeneous Markov processes
Chuchu Chen, Tonghe Dang, Jialin Hong +1
In order to give quantitative estimates for approximating the ergodic limit, we investigate probabilistic limit behaviors of time-averaging estimators of numerical discretizations…
Conservative methods for stochastic differential equations with a conserved quantity
Chuchu Chen, David Cohen, Jialin Hong
This paper proposes a novel conservative method for numerical computation of general stochastic differential equations in the Stratonovich sense with a conserved quantity. We show…