Related papers: On diffusion processes with drift in $L_{d+1}$

Lateral diffusion of molecules on surfaces plays a very important role in various biological processes, including lipid transport across the cell membrane, synaptic transmission and other phenomena such as exo- and endocytosis, signal…

In this paper, we study darning of general symmetric Markov processes by shorting some parts of the state space into singletons. A natural way to construct such processes is via Dirichlet forms restricted to the function space whose members…

Many important properties of granular fluids can be represented by a system of hard spheres with inelastic collisions. Traditional methods of nonequilibrium statistical mechanics are effective for analysis and description of the inelastic…

We study the Brownian motion of a classical particle in one-dimensional inhomogeneous environments where the transition probabilities follow quasiperiodic or aperiodic distributions. Exploiting an exact correspondence with the…

Mixing of materials is fundamental to many natural phenomena and engineering applications. The presence of discontinuous deformations - such as shear banding or wall slip - creates new mechanisms for mixing and transport beyond those…

We solve two problems related to the fluctuations of time-integrated functionals of Markov diffusions, used in physics to model nonequilibrium systems. In the first we derive and illustrate the appropriate boundary conditions on the…

We study the large deviations of current-type observables defined for Markov diffusion processes evolving in smooth bounded regions of $\mathbb{R}^d$ with reflections at the boundaries. We derive for these the correct boundary conditions…

We discuss a family of time-inhomogeneous two-dimensional diffusions, defined over a finite time interval $[0,T]$, having transition density functions that are expressible in terms of the integral kernels for negative exponentials of the…

We develop the theory of strong stationary duality for diffusion processes on compact intervals. We analytically derive the generator and boundary behavior of the dual process and recover a central tenet of the classical Markov chain theory…

Consider a spectrally positive Stable($1+\alpha$) process whose jumps we interpret as lifetimes of individuals. We mark the jumps by continuous excursions assigning "sizes" varying during the lifetime. As for Crump-Mode-Jagers processes…

This paper is divided into two parts. The first part reviews the formulae for f-divergences in the study of continuous-time Markov processes and explores their applications in areas such as stochastic stability, the second law of…

We introduce and analyze a model for the transport of particles or energy in extended lattice systems. The dynamics of the model acts on a discrete phase space at discrete times but has nonetheless some of the characteristic properties of…

For a class of stochastic differential equations with reflection for which a certain ${\mathbb{L}}^p$ continuity condition holds with $p>1$, it is shown that any weak solution that is a strong Markov process can be decomposed into the sum…

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…

Let $Mat_{\mathbb{C}}(K,N)$ be the space of $K\times N$ complex matrices. Let $\mathbf{B}_t$ be Brownian motion on $Mat_{\mathbb{C}}(K,N)$ starting from the zero matrix and $\mathbf{M}\in Mat_{\mathbb{C}}(K,N)$. We prove that, with $K\ge…

The diffraction of stochastic point sets, both Bernoulli and Markov, and of random tilings with crystallographic symmetries is investigated in rigorous terms. In particular, we derive the diffraction spectrum of 1D random tilings, of…

In a setting, where only "exit measures" are given, as they are associated with an arbitrary right continuous strong Markov process on a separable metric space, we provide simple criteria for the validity of Harnack inequalities for…

In this paper we intend to give a comprehensive approach of functional inequalities for diffusion processes under some "curvature" assumptions. Our notion of curvature coincides with the usual $\Gamma_2$ curvature of Bakry and Emery in the…

In the present work, we explore homogenization techniques for a class of switching diffusion processes whose drift and diffusion coefficients, and jump intensities are smooth, spatially periodic functions; we assume full coupling between…

In this paper a concentration inequality is proved for the deviation in the ergodic theorem in the case of discrete time observations of diffusion processes. The proof is based on the geometric ergodicity property for diffusion processes.…