Related papers: Superprocesses with Dependent Spatial Motion and G…

It has been proved by Bovier & Hartung [Elect. J. Probab. 19 (2014)] that the maximum of a variable-speed branching Brownian motion (BBM) in the weak correlation regime converges to a randomly shifted Gumbel distribution. The random shift…

In this paper we establish spatial central limit theorems for a large class of supercritical branching Markov processes with general spatial-dependent branching mechanisms. These are generalizations of the spatial central limit theorems…

We consider exponential functionals of a multi-dimensional Brownian motion with drift, defined via a collection of linear functionals. We give a characterization of the Laplace transform of their joint law as the unique bounded solution, up…

Consider a system of interacting particles indexed by the nodes of a graph whose vertices are equipped with marks representing parameters of the model such as the environment or initial data. Each particle takes values in a countable state…

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…

In this paper we study the maximal position process of branching Brownian motion in random spatial environment. The random environment is given by a process $\xi = \left(\xi(x)\right)_{x\in\mathbb{R}}$ satisfying certain conditions. We show…

As a result of nonequilibrium forces, purely repulsive self-propelled particles undergo macrophase separation between a dense and a dilute phase. We present a thorough study of the ordering kinetics of such motility-induced phase separation…

A finite one-dimensional microscopic model of a superfulid is presented. The model consists of interacting Bose particles with an additional impurity particle confined to a ring. Both semiclassical and exact quantum calculations reveal…

We give a probabilistic representation of a one-dimensional diffusion equation where the solution is discontinuous at $0$ with a jump proportional to its flux. This kind of interface condition is usually seen as a semi-permeable barrier.…

Let $(Z_n)$ be a supercritical branching process in a random environment $\xi$. We study the convergence rates of the martingale $W_n = Z_n/ E[Z_n| \xi]$ to its limit $W$. The following results about the convergence almost sur (a.s.), in…

We define the height process for super-critical continuous state branching processes with quadratic branching mechanism. It appears as a projective limit of Brownian motions with positive drift reflected at 0 and a>0 as a goes to infinity.…

We extend the class of $(\xi,\psi,K)$-superprocesses known so far by applying a simple transformation induced by a \lq\lq weight function\rq\rq\ for the one-particle motion. These transformed superprocesses may exist under weak conditions…

We find explicit upper bounds for the density of marginals of continuous diffusions where we assume that the diffusion coefficient is constant and the drift is solely assumed to be progressively measurable and locally bounded. In one…

We consider a processor sharing queue where the number of jobs served at any time is limited to $K$, with the excess jobs waiting in a buffer. We use random counting measures on the positive axis to model this system. The limit of this…

We propose diffusion-like equations with time and space fractional derivatives of the distributed order for the kinetic description of anomalous diffusion and relaxation phenomena, whose diffusion exponent varies with time and which,…

We analyze the microscopic model of quantum Brownian motion, describing a Brownian particle interacting with a bosonic bath through a coupling which is linear in the creation and annihilation operators of the bath, but may be a nonlinear…

This paper presents an {\it ab initio} derivation of the expression given by irreversible thermodynamics for the rate of entropy production for different classes of diffusive processes. The first class are Lorentz gases, where…

This paper discusses semiparametric inference on hypotheses on the cointegration and the attractor spaces for $I(1)$ linear processes with moderately large cross-sectional dimension. The approach is based on empirical canonical correlations…

Iterated Bessel processes R^\gamma(t), t>0, \gamma>0 and their counterparts on hyperbolic spaces, i.e. hyperbolic Brownian motions B^{hp}(t), t>0 are examined and their probability laws derived. The higher-order partial differential…

This paper studies small-time behavior at the supremum of a diffusion process. For a solution to the SDE $\mathrm{d} X_t=\mu(X_t)\mathrm{d} t+\sigma(X_t)\mathrm{d} W_t$ (where $W$ is a standard Brownian motion) we consider…