相关论文: On diffusion approximation with discontinuous coef…

Collective diffusion coefficient in a two-dimensional lattice gas on a nonhomogeneous substrate is investigated using variational approach. Particles reside at adsorption sites with different well depths potentials and jump randomly between…

We discuss diffusion properties of a dynamical system, which is characterised by long-tail distributions and finite correlations. The particle velocity has the stable L\'evy distribution; it is assumed as a jumping process (the kangaroo…

We consider a multicontinuum model in porous media applications, which is described as a system of coupled flow equations. The coupling between different continua depends on many factors and its modeling is important for porous media…

A system of interacting Brownian particles subject to short-range repulsive potentials is considered. A continuum description in the form of a nonlinear diffusion equation is derived systematically in the dilute limit using the method of…

We give a probabilistic numerical method for solving a partial differential equation with fractional diffusion and nonlinear drift. The probabilistic interpretation of this equation uses a system of particles driven by L\'evy alpha-stable…

Stochastic features of decay of a metastable phase have been investigated with the help of a new monodisperse approximation. This approximation is more precise than the already used one and namely it allows to give a very simple but rather…

A limit theorem for a sequence of diffusion processes on graphs is proved in a case when vary both parameters of the processes (the drift and diffusion coefficients on every edge and the asymmetry coefficients in every vertex), and…

We consider a Poisson equation in $\mathbb R^d$ for the elliptic operator corresponding to an ergodic diffusion process. Optimal regularity and smoothness with respect to the parameter are obtained under mild conditions on the coefficients.…

We provide examples of initial data which saturate the enhanced diffusion rates proved for general shear flows which are H\"{o}lder regular or Lipschitz continuous with critical points, and for regular circular flows, establishing the…

Stochastic reaction-diffusion models can be analytically studied on complex networks using the linear noise approximation. This is illustrated through the use of a specific stochastic model, which displays traveling waves in its…

We propose threshold diffusion processes as unique solutions to stochastic differential equations with step-function coefficients, and obtain explicit expressions for the conditional Laplace transform of the hitting times and the potential…

Diffusive approximations of Markov jump processes often fail to accurately capture large fluctuations. This is confounding, as the rare events triggered by these large fluctuations, such as the failure of electronic memories, are often the…

In this paper we study the randomized heat equation with homogeneous boundary conditions. The diffusion coeffcient is assumed to be a random variable and the initial condition is treated as a stochastic process. The solution of this…

Reaction diffusion systems describe the behaviour of dynamic, interacting, particulate systems. Quantum stochastic processes generalise Brownian motion and Poisson processes, having operator valued It\^{o} calculus machinery. Here it is…

In computational system biology, the mesoscopic model of reaction-diffusion kinetics is described by a continuous time, discrete space Markov process. To simulate diffusion stochastically, the jump coefficients are obtained by a…

The problem of the construction of strong approximations with a given order of convergence for jump-diffusion equations is studied. General approximation schemes are constructed for L\'evy type stochastic differential equation. In…

We consider stochastic systems involving general -- non-Gaussian and asymmetric -- stable processes. The random quantities, either a stochastic force or a waiting time in a random walk process, explicitly depend on the position. A…

Diffusion processes are studied theoretically for the case where the diffusion coefficient is itself a time and position dependent random function. We investigate how inhomogeneities and fluctuations of the diffusion coefficient affect the…

Deterministic diffusion in temporally oscillating convection is studied for particles with finite mass. The particles are assumed to obey a simple dissipative dynamical system and the particle diffusion is induced by the strange attractor.…

We investigate superdiffusion for stochastic processes generated by nonuniformly hyperbolic system models, in terms of the convergence of rescaled distributions to the normal distribution following the abnormal central limit theorem, which…