相关论文: Superdiffusive Central Limit Theorem for the Stoch…
This paper establishes a quantitative, uniform-in-time diffusion approximation for the joint law of a broad class of fully coupled multiscale stochastic systems. We derive a precise characterization of the limiting joint distribution as a…
We consider It\^o SDE $\d X_t=\sum_{j=1}^m A_j(X_t) \d w_t^j + A_0(X_t) \d t$ on $\R^d$. The diffusion coefficients $A_1,..., A_m$ are supposed to be in the Sobolev space $W_\text{loc}^{1,p} (\R^d)$ with $p>d$, and to have linear growth;…
This work contributes to the limited literature on estimating the diffusivity or drift coefficient of nonlinear SPDEs driven by additive noise. Assuming that the solution is measured locally in space and over a finite time interval, we show…
We consider reaction-diffusion equations that are stochastically forced by a small multiplicative noise term. We show that spectrally stable traveling wave solutions to the deterministic system retain their orbital stability if the…
The paper is devoted to the study of slightly supercritical active scalars with nonlocal diffusion. We prove global regularity for the surface quasi-geostrophic (SQG) and Burgers equations, when the diffusion term is supercritical by a…
Fragmentation population-balance equations (PBEs) describe how particle size distributions (PSDs) evolve under breakage and daughter fragment redistribution. From a standard self-similar fragmentation class we derive an \emph{exact…
Motivated by problems from statistical analysis for discretely sampled SPDEs, first we derive central limit theorems for higher order finite differences applied to stochastic process with arbitrary finitely regular paths. These results are…
Models defined by stochastic differential equations (SDEs) allow for the representation of random variability in dynamical systems. The relevance of this class of models is growing in many applied research areas and is already a standard…
In this paper, we consider a system of $k$ second order non-linear stochastic partial differential equations with spatial dimension $d \geq 1$, driven by a $q$-dimensional Gaussian noise, which is white in time and with some spatially…
The inviscid Burgers equation with random and spatially smooth forcing is considered in the limit when the size of the system tends to infinity. For the one-dimensional problem, it is shown both theoretically and numerically that many of…
Dynamical systems that are subject to continuous uncertain fluctuations can be modelled using Stochastic Differential Equations (SDEs). Controlling such system results in solving path constrained SDEs. Broadly, these problems fall under the…
In this paper, we investigate the existence and finite-time blow-up for the solution of a reaction-diffusion system of semilinear stochastic partial differential equations (SPDEs) subjected to a two-dimensional fractional Brownian motion…
An exact analysis is performed for the two-point correlation function C(r,t) in dissipative Burgers turbulence with bounded initial data, in arbitrary spatial dimension d. Contrary to the usual scaling hypothesis of a single dynamic length…
In this paper, we investigate the stochastic damped Burgers equation with multiplicative noise defined on the entire real line. We demonstrate the existence and uniqueness of a mild solution to the stochastic damped Burgers equation and…
It is widely believed that the breakdown of the Stokes-Einstein (SE) relation between the translational diffusivity and the shear viscosity in supercooled liquids is due to the development of dynamic heterogeneity i.e. the presence of both…
Anomalous diffusion and L\'evy flights, which are characterized by the occurrence of random discrete jumps of all scales, have been observed in a plethora of natural and engineered systems, ranging from the motion of molecules to climate…
The Lax equivalence theorem guarantees convergence of stable and consistent discretizations for linear hyperbolic partial differential equations (PDEs). For nonlinear problems, however, stability and consistency alone do not generally…
The paper establishes the strong convergence rates of a spatio-temporal full discretization of the stochastic wave equation with nonlinear damping in dimension one and two. We discretize the SPDE by applying a spectral Galerkin method in…
We introduce what we call the second-order Boltzmann-Gibbs principle, which allows to replace local functionals of a conservative, one-dimensional stochastic process by a possibly nonlinear function of the conserved quantity. This…
Deterministic rate equations are widely used in the study of stochastic, interacting particles systems. This approach assumes that the inherent noise, associated with the discreteness of the elementary constituents, may be neglected when…