Related papers: Occupation times for superprocesses in random envi…

Let $X=(X_t, t\geq 0)$ be a superprocess in a random environment described by a Gaussian noise $W=\{W(t,x), t\geq 0, x\in \mathbb{R}^d\}$ white in time and colored in space with correlation kernel $g(x,y)$. When $d\geq 3$, under the…

Let $X=(X_t, t\geq 0)$ be a superprocess in a random environment described by a Gaussian noise $W^g=\{W^g(t,x), t\geq 0, x\in \mathbb{R}^d\}$ white in time and colored in space with correlation kernel $g(x,y)$. We show that when $d=1$,…

The $(d,\alpha,\beta,\gamma)$-branching particle system consists of particles moving in $R^d$ according to a symmetric $\alpha$-stable L\'evy process $(0<\alpha\leq 2)$, splitting with a critical $(1+\beta)$-branching law $(0<\beta\leq 1)$,…

In the random acceleration process a point particle moving in one dimension is accelerated by Gaussian white noise with zero mean. Although several fundamental statistical properties of the motion have been analyzed in detail, the…

We extend results on time-rescaled occupation time fluctuation limits of the $(d,\alpha, \beta)$-branching particle system $(0<\alpha \leq 2, 0<\beta \leq 1)$ with Poisson initial condition. The earlier results in the homogeneous case…

Inspired by coarea formula in geometric measure theory, an occupation time formula for continuous semimartingales in $\mathbb{R}^{N}$ is proven. The occupation measure of a semimartingale, for $N\geq2$, is singular with respect to Lebesgue…

We consider the solution (u,\eta) of the white-noise driven stochastic partial differential equation with reflection on the space interval [0,1] introduced by Nualart and Pardoux. First, we prove that at any fixed time t>0, the measure…

This paper presents a set of results relating to the occupation time $\alpha(t)$ of a process $X(\cdot)$. The first set of results concerns exact characterizations of $\alpha(t)$ for $t\geq0$, e.g., in terms of its transform up to an…

We prove functional limits theorems for the occupation time process of a system of particles moving independently in $R^d$ according to a symmetric $\alpha$-stable L\'evy process, and starting off from an inhomogeneous Poisson point measure…

We introduce two natural notions for the occupation measure of a function $V$ with finite variation. The first yields a signed measure, and the second a positive measure. By comparing two versions of the change-of-variables formula, we show…

We consider a random sequential adsorption process on the one-dimensional lattice with nearest-neighbor exclusion. In this model, each site $s \in \mathbb{Z}$ starts empty and we will try to occupy it in time $t_s$, where…

We consider a super-Brownian motion $\{X_t, t\geq 0\}$ in a random environment described by a centered Gaussian field $\{W(t,x),t\geq 0, x\in\mathbb{R}^d\}$ whose correlation function is given by $\mathcal{C} (x,y)(t \wedge s)$. The process…

We present a systematic study of the statistics of the occupation time and related random variables for stochastic processes with independent intervals of time. According to the nature of the distribution of time intervals, the probability…

The aim of this work is to define and perform a study of local times of all Gaussian processes that have an integral representation over a real interval (that maybe infinite). Very rich, this class of Gaussian processes, contains Volterra…

We compute that the growth of the origin occupation-time variance up to time t in dimension d=2 with respect to asymmetric simple exclusion in equilibrium with density 1/2 is in a certain sense at least t(log(log t)) for general rates, and…

Assume that $T$ is a conservative ergodic measure preserving transformation of the infinite measure space $(X,\mathcal{A},\mu)$.We study the asymptotic behaviour of occupation times of certain subsets of infinite measure. Specifically, we…

We consider a new type of lookdown processes where spatial motion of each individual is influenced by an individual noise and a common noise, which could be regarded as an environment. Then a class of probability measure-valued processes on…

We show that the law of the overall supremum $\bar{X}_t=\sup_{s\le t}X_s$ of a L\'evy process $X$ before the deterministic time $t$ is equivalent to the average occupation measure $\mu_t(dx)=\int_0^t\p(X_s\in dx)\,ds$, whenever 0 is regular…

For a Dawson-Watanabe superprocess $X$ on $\mathbb{R}^d$, it is shown in Perkins (1990) that if the underlying spatial motion belongs to a certain class of L\'evy processes that admit jumps, then with probability one the closed support of…

For a Dawson-Watanabe superprocess $X$ on $\mathbb{R}^d$, it is shown in Perkins (1990) that if the underlying spatial motion belongs to a certain class of L\'evy processes that admit jumps, then with probability one the closed support of…