Brownian motions in a Lie group

Self-similarity and fractional Brownian motions on Lie groups

The goal of this paper is to define and study a notion of fractional Brownian motion on a Lie group. We define it as at the solution of a stochastic differential equation driven by a linear fractional Brownian motion. We show that this process has stationary increments and satisfies a local self-similar property. Furthermore the Lie groups for which this self-similar property is global are char...

Bouncing skew Brownian motions

We consider two skew Brownian motions, driven by the same Brownian motion, with different starting points and different skewness coefficients. In [13], the evolution of the distance between the two processes, in local time scale and up to their first hitting time is shown to satisfy a stochastic differential equation with jumps. The jumps of this S.D.E. are naturally driven by the excursion pro...

Nonintersecting Planar Brownian Motions

In this paper we construct a measure on pairs of Brownian motions starting at the same point conditioned so their paths do not intersect. The construction of this measure is a start towards the rigorous understanding of nonintersecting Brownian motions as a conformal eld. Let B 1 ; B 2 be independent Brownian motions in R 2 starting at distinct points on the unit circle. Let T j r be the rst ti...

Perturbed Brownian Motions

Introduction to Brownian Motions

This paper aims to present some basic facts about Brownian Motions. It will assume a basic familiarity with probability and random variables. It will begin by defining Brownian Motion in one dimension on the dyadic rationals using a countable number of random variables and then proceed to generalize this to the real line using a continuity argument. Some other consequences of continuity will be...