No Arabic abstract
Let $D$ be an unbounded domain in $RR^d$ with $dgeq 3$. We show that if $D$ contains an unbounded uniform domain, then the symmetric reflecting Brownian motion (RBM) on $overline D$ is transient. Next assume that RBM $X$ on $overline D$ is transient and let $Y$ be its time change by Revuz measure ${bf 1}_D(x) m(x)dx$ for a strictly positive continuous integrable function $m$ on $overline D$. We further show that if there is some $r>0$ so that $Dsetminus overline {B(0, r)}$ is an unbounded uniform domain, then $Y$ admits one and only one symmetric diffusion that genuinely extends it and admits no killings. In other words, in this case $X$ (or equivalently, $Y$) has a unique Martin boundary point at infinity.
A time-changed mixed fractional Brownian motion is an iterated process constructed as the superposition of mixed fractional Brownian motion and other process. In this paper we consider mixed fractional Brownian motion of parameters a, b and Hin(0, 1) time-changed by two processes, gamma and tempered stable subordinators. We present their main properties paying main attention to the long range dependence. We deduce that the fractional Brownian motion time-changed by gamma and tempered stable subordinators has long range dependence property for all Hin(0, 1).
We study a natural continuous time version of excited random walks, introduced by Norris, Rogers and Williams about twenty years ago. We obtain a necessary and sufficient condition for recurrence and for positive speed. This is analogous to results for excited (or cookie) random walks.
We prove the existence of the intersection local time for two independent, d -dimensional fractional Brownian motions with the same Hurst parameter H. Assume d greater or equal to 2, then the intersection local time exists if and only if Hd<2.
Roughly speaking, a space with varying dimension consists of at least two components with different dimensions. In this paper we will concentrate on the one, which can be treated as $mathbb{R}^3$ tying a half line not contained by $mathbb{R}^3$ at the origin. The aim is twofold. On one hand, we will introduce so-called distorted Brownian motions on this space with varying dimension (dBMVDs in abbreviation) and study their basic properties by means of Dirichlet forms. On the other hand, we will prove the joint continuity of the transition density functions of these dBMVDs and derive the short-time heat kernel estimates for them.
In this paper we introduce a new method for the simulation of the exit time and position of a $delta$-dimensional Brownian motion from a domain. The main interest of our method is that it avoids splitting time schemes as well as inversion of complicated series. The idea is to use the connexion between the $delta$-dimensional Bessel process and the $delta$-dimensional Brownian motion thanks to an explicit Bessel hitting time distribution associated with a particular curved boundary. This allows to build a fast and accurate numerical scheme for approximating the hitting time. Numerical comparisons with existing methods are performed.