Related papers: On diffusion processes with drift in a Morrey clas…

It is well-known under the name of `periodic homogenization' that, under a centering condition of the drift, a periodic diffusion process on R^d converges, under diffusive rescaling, to a d-dimensional Brownian motion. Existing proofs of…

We consider a time inhomogeneous strong Markov process $(\xi_t)_{t\ge 0}$ taking values in a Polish state space whose semigroup has a $T$-periodic structure. We give simple conditions which imply ergodicity of the grid chain…

For a general class of diffusion processes with multiplicative noise, describing a variety of physical as well as financial phenomena, mostly typical of complex systems, we obtain the analytical solution for the moments at all times. We…

In this note we study the behaviour as $s\to 0^+$ of some semigroup based Besov seminorms associated with a non-symmetric and hypoelliptic diffusion with a drift. Our results generalise a previous one of Maz'ya and Shaposhnikova for the…

We present some new results on sample path optimality for the ergodic control problem of a class of non-degenerate diffusions controlled through the drift. The hypothesis most often used in the literature to ensure the existence of an a.s.…

We consider the question of estimating the drift and the invariant density for a large class of scalar ergodic diffusion processes, based on continuous observations, in $\sup$-norm loss. The unknown drift $b$ is supposed to belong to a…

We present regularity results for nonlinear drift-diffusion equations of porous medium type (together with their incompressible limit). We relax the assumptions imposed on the drift term with respect to previous results and additionally…

Let $V$ be a two sided random walk and let $X$ denote a real valued diffusion process with generator ${1/2}e^{V([x])}\frac{d}{dx}(e^{-V([x])}\frac{d}{dx})$. This process is known to be the continuous equivalent of the one dimensional random…

This paper deals with ergodic theorems for particular time-inhomogeneous Markov processes, whose the time-inhomogeneity is asymptotically periodic. Under a Lyapunov/minorization condition, it is shown that, for any measurable bounded…

In this paper a new dissimilarity measure to identify groups of assets dynamics is proposed. The underlying generating process is assumed to be a diffusion process solution of stochastic differential equations and observed at discrete time.…

The paper presents new simple sharp bounds for transition density functions for time-homogeneous diffusions processes. The bounds are obtained under mild conditions on the drift and diffusion coefficients, extending and substantially…

In the paper, we study a new rate of convergence estimate for homogeneous discrete-time nonlinear Markov chains based on the Markov-Dobrushin condition. This result generalizes the convergence estimates for any positive number of transition…

We consider a cross-diffusion system for which the diffusion of each species is governed solely by the aggregate density through a pressure law of logarithmic or fast diffusion type. The model is set over a one dimensional bounded interval,…

We prove the existence of weak solutions of It\^o's stochastic time dependent equations with irregular diffusion and drift terms of Morrey spaces. Weak uniqueness (generally conditional) and a conjecture pertaining to strong solutions are…

We address the question of the trends to equilibrium for a large class C of relativistic diffusions. We show the existence of a spectral gap using the Lyapounov method and deduce the exponential decay of the distance to equilibrium in…

We demonstrate the non-ergodicity of a simple Markovian stochastic processes with space-dependent diffusion coefficient $D(x)$. For power-law forms $D(x) \simeq|x|^{\alpha}$, this process yield anomalous diffusion of the form $\ < x^2(t)\ >…

We investigate energy diffusion in long-range interacting spin systems, where the interaction decays algebraically as $V(r) \propto r^{-\alpha}$ with the distance $r$ between the sites. We consider prototypical spin systems, the transverse…

We consider diffusion processes with a spatially varying diffusivity giving rise to anomalous diffusion. Such heterogeneous diffusion processes are analysed for the cases of exponential, power-law, and logarithmic dependencies of the…

When the unconditioned process is a diffusion process $X(t)$ of drift $\mu(x)$ and of diffusion coefficient $D=1/2$, the local time $A(t)= \int_{0}^{t} d\tau \delta(X(\tau)) $ at the origin $x=0$ is one of the most important time-additive…

Stationary distributions of multivariate diffusion processes have recently been proposed as probabilistic models of causal systems in statistics and machine learning. Motivated by these developments, we study stationary multivariate…