Related papers: Diffusion limit for a stochastic kinetic problem w…

The long time behavior of an absorbed Markov process is well described by the limiting distribution of the process conditioned to not be killed when it is observed. Our aim is to give an approximation's method of this limit, when the…

We consider a generalization of classical results of Freidlin and Wentzell to the case of time dependent dissipative drifts. We show the convergence of diffusions with multiplicative noise in the zero limit of a diffusivity parameter to the…

We address the now classical problem of a diffusion process that crosses over from a ballistic behavior at short times to a fractional diffusion (sub- or super-diffusion) at longer times. Using the standard non-Markovian diffusion equation…

We study the diffusion-reaction-advection model for mobile chemical species together with the dissolution and precipitation of immobile species in a porous medium at the micro-scale. This leads to a system of semilinear parabolic partial…

A multiplicative stochastic process with the lower bound lognormally distributed is investigated. For the process, the model is constructed, and its distribution function (involving four parameters) and the related statistical properties…

This paper is concerned with the large deviation principle of the non-local fractional stochastic reaction-diffusion equation with a polynomial drift of arbitrary degree driven by multiplicative noise defined on unbounded domains. We first…

Stochastic computational models in the form of pure jump processes occur frequently in the description of chemical reactive processes, of ion channel dynamics, and of the spread of infections in populations. For spatially extended models,…

We analyze a pair of diffusion equations which are derived in the infinite system--size limit from a microscopic, individual--based, stochastic model. Deviations from the conventional Fickian picture are found which ultimately relate to the…

We show the variational convergence of an irreversible Markov jump process describing a finite stochastic particle system to the solution of a countable infinite system of deterministic time-inhomogeneous quadratic differential equations…

We consider multiple time scales systems of stochastic differential equations with small noise in random environments. We prove a quenched large deviations principle with explicit characterization of the action functional. The random medium…

This paper studies diffusion processes constrained to the positive orthant under infinitesimal changes in the drift. Our first main result states that any constrained function and its (left) drift-derivative is the unique solution to an…

We present an asymptotic preserving scheme based on a micro-macro decomposition for stochastic linear transport equations in kinetic and diffusive regimes. We perfom a mathematical analysis and prove that the scheme is uniformly stable with…

Parametric estimation for diffusion processes is considered for high frequency observations over a fixed time interval. The processes solve stochastic differential equations with an unknown parameter in the diffusion coefficient. We find…

This article deals with the limit distribution for a stochastic differential equation driven by a non-symmetric cylindrical $\alpha$-stable process. Under suitable conditions, it is proved that the solution of this equation converges weakly…

I discuss the so-called stochastic individual based model of adaptive dynamics and in particular how different scaling limits can be obtained by taking limits of large populations, small mutation rate, and small effect of single mutations…

Stochastic maximum principle of nonlinear controlled forward-backward systems, where the set of strict (classical) controls need not be convex and the diffusion coefficient depends explicitly on the variable control, is an open problem…

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 consider the adaptive test for the parameter change in discretely observed ergodic diffusion processes based on the cusum test. Using two test statistics based on the two quasi-log likelihood functions of the diffusion parameter and the…

In sustained growth with random dynamics stationary distributions can exist without detailed balance. This suggests thermodynamical behavior in fast growing complex systems. In order to model such phenomena we apply both a discrete and a…

We consider the problem of minimizing a convex function that is evolving according to unknown and possibly stochastic dynamics, which may depend jointly on time and on the decision variable itself. Such problems abound in the machine…