Related papers: Smooth densities for stochastic differential equat…

A recent paper of Melbourne & Stuart, A note on diffusion limits of chaotic skew product flows, Nonlinearity 24 (2011) 1361-1367, gives a rigorous proof of convergence of a fast-slow deterministic system to a stochastic differential…

We investigate the existence of a robust, i.e., continuous, representation of the conditional distribution in a stochastic filtering model for multidimensional correlated jump-diffusions. Even in the absence of jumps, it is known that in…

Semilinear stochastic evolution equations with multiplicative L\'evy noise and monotone nonlinear drift are considered. Unlike other similar works, we do not impose coercivity conditions on coefficients. We establish the continuous…

The stochastic partial differential equation analyzed in this work is the Cahn-Hilliard equation perturbed by an additive fractional white noise (fractional in time and white in space). We work in the case of one spatial dimension and apply…

We consider a process given by a two-dimensional fractional Brownian motion with Hurst parameter 1/3 < H < 1/2, along with an associated L\'evy area, and prove the smoothness of a density for this process with respect to Lebesgue measure.

We are concerned with the absolute continuity of stationary distributions corresponding to some piecewise deterministic Markov process, being typically encountered in biological models. The process under investigation involves a…

We generalize the notion of the submartingale property and Doob's inequality. Furthermore, we show how the latter leads to new inequalities for several stochastic processes: certain time series, Levy processes, random walks, processes with…

We consider a parabolic partial differential equation that can be understood as a simple model for crowds flows. Our main assumption is that the diffusivity and the source/sink term vanish at the same point; the nonhomogeneous term is…

We exhibit conditions under which the flow of marginal distributions of a discontinuous semimartingale $\xi$ can be matched by a Markov process, whose infinitesimal generator is expressed in terms of the local characteristics of $\xi$. Our…

Consider a system of particles performing nearest neighbor random walks on the lattice $\ZZ$ under hard--core interaction. The rate for a jump over a given bond is direction--independent and the inverse of the jump rates are i.i.d. random…

The aim of this paper is to obtain estimates for the density of the law of a specific nonlinear diffusion process at any positive bounded time. This process is issued from kinetic theory and is called Landau process, by analogy with the…

The study of time-inhomogeneous Markov jump processes is a traditional topic within probability theory that has recently attracted substantial attention in various applications. However, their flexibility also incurs a substantial…

We establish a local martingale $M$ associate with $f(X,Y)$ under some restrictions on $f$, where $Y$ is a process of bounded variation (on compact intervals) and either $X$ is a jump diffusion (a special case being a L\'evy process) or $X$…

We consider a mixed stochastic differential equation $d{X_t}=a(t,X_t)d{t}+b(t,X_t) d{W_t}+c(t,X_t)d{B^H_t}$ driven by independent multidimensional Wiener process and fractional Brownian motion. Under Hormander type conditions we show that…

This paper reviews various applications of the theory of smooth dynamical systems to conceptual problems of nonequilibrium statistical mechanics. We adopt a new point of view which has emerged progressively in recent years, and which takes…

We consider a 2D stochastic modified Swift-Hohenberg equations with multiplicative noise and periodic boundary. First, we establish the existence of local and global martingale and pathwise solutions in the regular Sobolev space $H^{2m}$…

The consistency across scales of a recently developed mathematical thermodynamic structure, between a continuous stochastic nonlinear dynamical system (diffusion process with Langevin or Fokker-Planck equations) and its emergent discrete,…

We prove the global asymptotic equivalence between the experiments generated by the discrete (high frequency) or continuous observation of a path of a time inhomogeneous jump-diffusion process and a Gaussian white noise experiment. Here,…

We prove three results on the existence of densities for the laws of finite dimensional functionals of the solutions of the stochastic Navier-Stokes equations in dimension 3. In particular, under very mild assumptions on the noise, we prove…

In this note, we establish optimal lower and upper Gaussian bounds for the density of the solution to a class of stochastic integral equations driven by an additive spatially homogeneous Gaussian random field. The proof is based on the…