Related papers: On small-noise equations with degenerate limiting …
Consider a multidimensional diffusion process $X=\{X\left(t\right) :t\in\lbrack0,1]\}$. Let $\varepsilon>0$ be a \textit{deterministic}, user defined, tolerance error parameter. Under standard regularity conditions on the drift and…
We consider a nonlinear differential equation under the combined influence of small state-dependent Brownian perturbations of size $\varepsilon$, and fast periodic sampling with period $\delta$; $0<\varepsilon, \delta \ll 1$. Thus, state…
This paper concerns the use of asymptotic expansions for the efficient solving of forward and inverse problems involving a nonlinear singularly perturbed time-dependent reaction--diffusion--advection equation. By using an asymptotic…
In this paper we study short time asymptotics of a density function of the solution of a stochastic differential equation driven by fractional Brownian motion with Hurst parameter $H \in (1/2, 1)$ when the coefficient vector fields satisfy…
This paper provides a large deviation principle for Non-Markovian, Brownian motion driven stochastic differential equations with random coefficients. Similar to Gao and Liu \cite{GL}, this extends the corresponding results collected in…
We study Langevin dynamics with stochastic diffusivity arising from fluctuations of the surrounding medium. The diffusivity is modeled as Ornstein-Uhlenbeck process driven by symmetric dichotomous noise, which confines it to a finite…
Recent years have witnessed significant progress in developing effective training and fast sampling techniques for diffusion models. A remarkable advancement is the use of stochastic differential equations (SDEs) and their…
We consider a class of slow-fast processes on a connected complete Riemannian manifold $M$.The limiting dynamics as the scale separation goes to $\infty$ is governed by the averaging principle. Around this limit, we prove large deviation…
The main goal of this article is to study the effect of small, highly nonlinear, unbounded drifts (small time large deviation principle (LDP) based on exponential equivalence arguments) for a class of stochastic partial differential…
We prove a large deviation principle for the slow-fast rough differential equations under the controlled rough path framework. The driver rough paths are lifted from the mixed fractional Brownian motion with Hurst parameter $H\in…
We consider SDEs of the form $dX_t = |f(X_t)|/t^{\gamma} dt+1/t^{\gamma} dB_t$, where $f(x)$ behaves comparably to $|x|^k$ in a neighborhood of the origin, for $k\in [1,\infty)$. We show that there exists a threshold value…
We consider an SDE in R^m of the type dX(t)=a(X(t))dt+dU(t) with a L\'evy process U and study the problem for the distribution of a solution to be regular in various senses. We do not impose any specific conditions on the L\'evy measure of…
Stochastic partial differential equations driven by Poisson random measures (PRM) have been proposed as models for many different physical systems, where they are viewed as a refinement of a corresponding noiseless partial differential…
We study small noise large deviation asymptotics for stochastic differential equations with a multiplicative noise given as a fractional Brownian motion $B^H$ with Hurst parameter $H>\frac12$. The solutions of the stochastic differential…
We consider parameter estimation of the reaction term for a second order linear parabolic stochastic partial differential equation in two space dimensions driven by a $Q$-Wiener process under small diffusivity. We first construct an…
Large deviations principles characterize the exponential decay rates of the probabilities of rare events. Cerrai and Rockner [13] proved that systems of stochastic reaction-diffusion equations satisfy a large deviations principle that is…
In this paper, we study the asymptotic behavior of a semi-linear slow-fast stochastic partial differential equation with singular coefficients. Using the Poisson equation in Hilbert space, we first establish the strong convergence in the…
We consider a parameter estimation problem for one dimensional stochastic heat equations, when data is sampled discretely in time or spatial component. We prove that, the real valued parameter next to the Laplacian (the drift), and the…
Semilinear parabolic partial differential equations (PDEs) are fundamental to modeling complex dynamical systems across scientific domains. The Deep Backward Stochastic Differential Equation (BSDE) method is a promising approach for…
The large-time asymptotics of the density matrix solving a drift-diffusion-Poisson model for the spin-polarized electron transport in semiconductors is proved. The equations are analyzed in a bounded domain with initial and Dirichlet…