Related papers: Statistical Analysis of Some Evolution Equations D…

We consider a d-dimensional stochastic differential equation with additive noise and a drift coefficient which is assumed only to be a bounded Borel function. We show that, for almost all choices of the driving Brownian path, the equation…

This paper considers stochastic population dynamics driven by Levy noise. The contributions of this paper lie in that (a) Using Khasminskii-Mao theorem, we show that the stochastic differential equation associated with the model has a…

The non-linear dynamics of long-wavelength cosmological fluctuations may be phrased in terms of an effective classical, but stochastic evolution equation. The stochastic noise represents short-wavelength modes that continually redshift into…

We present simple classical dynamical models to address the question of introducing a stochastic nature in a time variable. These models include noise in the time variable but not in the "space" variable, which is opposite to the normal…

This paper is devoted to studying stochastic parabolic evolution equations with additive noise in Banach spaces of M-type 2. We construct both strict and mild solutions possessing very strong regularities. First, we consider the linear…

This paper is mainly concerned with a kind of fractional stochastic evolution equations driven by L\'evy noise in a bounded domain. We first state the well-posedness of the problem via iterative approximations and energy estimates. Then,…

Frequency-dependent selection reflects the interaction between different species as they battle for limited resources in their environment. In a stochastic evolutionary game the species relative fitnesses guides the evolutionary dynamics…

In this article we give sufficient and necessary conditions for the existence of a weak and mild solution to stochastic evolution equations with (general) L\'{e}vy noise taking values in the dual of a nuclear space. As part of our approach…

Stochastic inverse problems considered in this article consist of estimating the probability distributions of intrinsically random inputs of computer models. These estimations are based on observable outputs affected by model noise, and…

The technique of stochastic solutions, previously used for deterministic equations, is here proposed as a solution method for partial differential equations driven by distribution-valued noises.

This paper establishes results on the existence and uniqueness of solutions to McKean-Vlasov equations, also called mean-field stochastic differential equations, in an infinite-dimensional Hilbert space setting with irregular drift. Here,…

One proves here the backward uniqueness of solutions to stochastic semilinear parabolic equations and also for the tamed Navier-Stokes equations driven by linearly multiplicative Gaussian noises. Applications to approximate controllability…

A new class of random partial differential equations of parabolic type is considered, where the stochastic term consists of an irregular noisy drift, not necessarily Gaussian, for which a suitable interpretation is provided. After freezing…

With the rapid increase of valuable observational, experimental and simulating data for complex systems, great efforts are being devoted to discovering governing laws underlying the evolution of these systems. However, the existing…

We consider the 2D stochastic Navier-Stokes equations driven by noise that has the regularity of space-time white noise but doesn't exactly coincide with it. We show that, provided that the intensity of the noise is sufficiently weak at…

We establish a new version of the stochastic Strichartz estimate for the stochastic convolution driven by jump noise which we apply to the stochastic nonlinear Schr\"{o}dinger equation with nonlinear multiplicative jump noise in the Marcus…

A stochastic linear transport equation with multiplicative noise is considered and the question of no-blow-up is investigated. The drift is assumed only integrable to a certain power. Opposite to the deterministic case where smooth initial…

We give a overview of stochastic models of evolution that have found applications in genetics, ecology and linguistics for an audience of nonspecialists, especially statistical physicists. In particular, we focus mostly on neutral models in…

We consider statistics for stochastic evolution equations in Hilbert space with emphasis on stochastic partial differential equations (SPDEs). We observe a solution process under additional measurement errors and want to estimate a real or…

In this paper, we study the long-time stability behavior of a class of linear stochastic evolution equations in a Hilbert space with multiplicative noise. Explicit sufficient conditions for $p$-th moment and almost sure exponential…