Related papers: Central limit theorem and moderate deviations for …
In this paper, we establish a moderate deviation principle for stochastic models of two-dimensional second grade fluids driven by L\'evy noise. We will adopt the weak convergence approach. Because of the appearance of jumps, this result is…
The influence of small random perturbations on a deterministic dynamical system with a locally stable equilibrium is considered. The perturbed system is described by the It\^{o} stochastic differential equation. It is assumed that the noise…
In this paper, the optimal control for discrete-time systems driven by fractional noises is studied. A stochastic maximum principle is obtained by introducing a backward stochastic difference equation contains both fractional noises and the…
Recent work in dynamic causal inference introduced a class of discrete-time stochastic processes that generalize martingale difference sequences and arrays as follows: the random variates in each sequence have expectation zero given certain…
The Cahn-Hilliard equation describes phase separation in binary liquids. Here we study this equation with spatially-varying sources and stirring, or advection. We specialize to symmetric mixtures and time-independent sources and discuss…
In this paper we develop a white noise framework for the study of stochastic partial differential equations driven by a d-parameter (pure jump) Levy white noise. As an example we use this theory to solve the stochastic Poisson equation with…
Considering a linear parabolic stochastic partial differential equation driven by impulsive space time noise, dX_t+AX_t dt= Q^{1/2}dZ_t, X_0=x_0\in H, t\in [0,T], we approximate the distribution of X_T. (Z_t)_{t\in[0,T]} is an impulsive…
We provide a simple proof for of the central limit theorem for the number of vertices in the giant for super-critical stochastic block model using the breadth-first walk of Konarovskyi, Limic and the author (2024). Our approach follows the…
We establish an optimal strong convergence rate of a fully discrete numerical scheme for second order parabolic stochastic partial differential equations with monotone drifts, including the stochastic Allen-Cahn equation, driven by an…
In this paper, we prove the moderate deviations principle (MDP) for a general system of slow-fast dynamics. We provide a unified approach, based on weak convergence ideas and stochastic control arguments, that cover both the averaging and…
We prove a quenched local central limit theorem for continuous-time random walks in $\mathbb Z^d, d\ge 2$, in a uniformly-elliptic time-dependent balanced random environment which is ergodic under space-time shifts. We also obtain Gaussian…
We study the asymptotic behavior, uniform-in-time, of a non-linear dynamical system under the combined effects of fast periodic sampling with period $\delta$ and small white noise of size $\varepsilon,\thinspace 0<\varepsilon,\delta \ll 1$.…
We study an Allen-Cahn equation perturbed by a multiplicative stochastic noise which is white in time and correlated in space. Formally this equation approximates a stochastically forced mean curvature flow. We derive uniform energy bounds…
We consider the perturbation of elliptic operators of the form $P(\bx,\bD)$ by random, rapidly varying, sufficiently mixing, potentials of the form $q(\frac{\bx}\eps,\omega)$. We analyze the source and spectral problems associated to such…
In this paper, we consider a semi-linear stochastic strongly damped wave equation driven by additive Gaussian noise. Following a semigroup framework, we establish existence, uniqueness and space-time regularity of a mild solution to such…
Based on relative energy estimates, we study the stability of solutions to the Cahn-Hilliard equation with concentration dependent mobility with respect to perturbations. As a by-product of our analysis, we obtain a weak-strong uniqueness…
We study the small noise asymptotic for stochastic Burgers equations on $(0,1)$ with Dirichlet boundary condition. We consider the case that the noise is more singular than space-time white noise. We let the noise magnitude $\sqrt{\epsilon}…
A non-classical formulation of the central limit theorem is given for sequences of independent random variables with finite second moments. Singular sequences whose members all have a degenerate or normal distribution are excluded from…
In this paper, we give sufficient conditions to establish central limit theorems for boundary estimates of Poisson point processes. The considered estimates are obtained by smoothing some bias corrected extreme values of the point process.…
It is a well established result that, in classical dynamical systems with sufficient time-scale separation, the fast chaotic degrees of freedom are well modeled by (Gaussian) white noise. In this paper, we present the stochastic dynamical…