相关论文: Doubly probabilistic representation for the stocha…
Nonlinear stochastic differential equations generating signals with 1/f spectrum have been used so far to describe socio-economical systems. In this paper we consider the motion of a Brownian particle in an inhomogeneous environment such…
We study the effect of Gaussian perturbations on a hyperbolic partial differential equation with double characteristics in two spatial dimensions. The coefficients of our partial differential operator depend polynomially on the space…
In this paper we show that solutions of stochastic partial differential equations driven by Brownian motion can be approximated by stochastic partial differential equations forced by pure jump noise/random kicks. Applications to stochastic…
We prove the existence and uniqueness of probabilistically strong solutions to stochastic porous media equations driven by time-dependent multiplicative noise on a general measure space $(E, \mathscr{B}(E), \mu)$, and the Laplacian replaced…
Numerical methods for stochastic partial differential equations typically estimate moments of the solution from sampled paths. Instead, we shall directly target the deterministic equations satisfied by the first and second moments, as well…
We present a stochastic model for amplifying, diffusive media like, for instance, random lasers. Starting from a simple random-walk model, we derive a stochastic partial differential equation for the energy field with contains a…
The purpose of the present note consists of first showing a uniqueness result for a stochastic Fokker-Planck equation under very general assumptions. In particular, the second order coefficients may be just measurable and degenerate. We…
We discuss maximum likelihood estimation of parameters for models governed by a stochastic differential equation driven by a mixed fractional Brownian motion with random effects.
We prove a priori bounds for solutions of singular stochastic porous media equations with multiplicative noise in their natural $L^1$-based regularity class. We consider the first singular regime, i.e.~noise of space-time regularity…
A non-negative Markovian solution is constructed for a class of stochastic generalized porous media equations with reflection. To this end, some regularity properties and a comparison theorem are proved for stochastic generalized porous…
The characterization of the covariance function of the solution process to a stochastic partial differential equation is considered in the parabolic case with multiplicative L\'evy noise of affine type. For the second moment of the mild…
Exact generalized stochastic representation of deterministic interaction between two dynamical (quantum or classical) systems is derived which helps when considering one of them to replace another by equivalent commutative ($c$-number…
We consider parabolic stochastic partial differential equations driven by white noise in time. We prove exponential convergence of the transition probabilities towards a unique invariant measure under suitable conditions. These conditions…
We consider the generalized almost periodic homogenization problem for two different types of stochastic conservation laws with oscillatory coefficients and multiplicative noise. In both cases the stochastic perturbations are such that the…
This paper is devoted to the study of the stochastic-periodic homogenization of Poisson-Nernst-Planck equations in porous media. It is shown by the stochastic two-scale convergence method extended to periodic surfaces that results in a…
In this note, we establish a bi-parameter linear localization of the one-dimensional stochastic wave equation with a multiplicative space-time white noise forcing.
This article deals with the approximation of a stochastic partial differential equation (SPDE) via amplitude equations. We consider an SPDE with a cubic nonlinearity perturbed by a general multiplicative noise that preserves the constant…
We prove finite speed of propagation for stochastic porous media equations perturbed by linear multiplicative space-time rough signals. Explicit and optimal estimates for the speed of propagation are given. The result applies to any…
Diffusion with stochastic transport is investigated here when the random driving process is a very general Gaussian process, including Fractional Brownian motion. The purpose is the comparison with a deterministic PDE, which in certain…
We study the role of multiplicative colored noise for different values of the correlation time $\tau_c$ in the dynamics of two competing species, described by generalized Lotka-Volterra equations. The multiplicative colored noise models the…