相关论文: Averaging in the case of multiple invariant measur…

Motivated by applications to mathematical biology, we study the averaging problem for slow-fast systems, {\em in the case in which the fast dynamics is a stochastic process with multiple invariant measures}. We consider both the case in…

We study the validity of an averaging principle for a slow-fast system of stochastic reaction diffusion equations. We assume here that the coefficients of the fast equation depend on time, so that the classical formulation of the averaging…

The asymptotic behavior for fully coupled multiscale stochastic systems becomes much complicated when the fast processes do not locate in a compact space. An example is constructed to show that the averaged coefficients may become…

We present the validity of stochastic averaging principle for non-autonomous slow-fast stochastic differential equations (SDEs) whose fast motions admit random periodic solutions. Our investigation is motivated by some problems arising from…

This work studies the averaging principle for a fully coupled two time-scale system, whose slow process is a diffusion process and fast process is a purely jumping process on an infinitely countable state space. The ergodicity of the fast…

In this paper, a class of piecewise deterministic Markov processes with underlying fast dynamic is studied. Using a "penalty method" , an averaging result is obtained when the underlying dynamic is infinitely accelerated. The features of…

The interplay between bifurcations and random switching processes of vector fields is studied. More precisely, we provide a classification of piecewise deterministic Markov processes arising from stochastic switching dynamics near fold,…

Equation with the symmetric integral with respect to stochastic measure is considered. For the integrator, we assume only $\sigma$-additivity in probability and continuity of the paths. It is proved that the averaging principle holds for…

In this work we study the averaging principle for non-autonomous slow-fast systems of stochastic differential equations. In particular in the first part we prove the averaging principle assuming the sublinearity, the Lipschitzianity and the…

In this paper, we study a class of multiscale McKean-Vlasov stochastic systems where the entire system depends on the distribution of the fast component. First of all, by the Poisson equation method we prove that the slow component…

In this paper, we consider a class of nonautonomous multi-scale stochastic partial differential equations with fully local monotone coefficients. By introducing the evolution system of measures for time-inhomogeneous Markov semigroups, we…

We study the asymptotic behavior for an inhomogeneous multiscale stochastic dynamical system with non-smooth coefficients. Depending on the averaging regime and the homogenization regime, two strong convergences in the averaging principle…

We establish convergence to an invariant measure as time tends to infinity, for a large class of (possibly non-Markovian) stochastic volatility models. Our arguments are based on a novel coupling idea for Markov chains which also extends to…

We consider a deterministic system with two conserved quantities and infinity many invariant measures. However the systems possess a unique invariant measure when enough stochastic forcing and balancing dissipation are added. We then show…

A diffusion taking value in probability measures on a graph with a vertex set $V$, $\sum_{i\in V}x_i\delta_i$, is studied. The masses on each vertices satisfy the stochastic differential equation of the form $dx_i=\sum_{j\in…

This simple note lays out a few observations which are well known in many ways but may not have been said in quite this way before. The basic idea is that when comparing two different Markov chains it is useful to couple them is such a way…

In this paper, we aim to develop the averaging principle for a slow-fast system of stochastic reaction-diffusion equations driven by Poisson random measures. The coefficients of the equation are assumed to be functions of time, and some of…

An approach for the description of stochastic systems is derived. Some of the variables in the system are studied forward in time, others backward in time. The approach is based on a perturbation expansion in the strength of the coupling…

We prove a stochastic averaging theorem for stochastic differential equations in which the slow and the fast variables interact. The approximate Markov fast motion is a family of Markov process with generator ${\mathcal L}_x$ for which we…

We prove an invariance principle for non-stationary random processes and establish a rate of convergence under a new type of mixing condition. The dependence is exponentially decaying in the gap between the past and the future and is…