Maximal Brownian motions

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...

Are fractional Brownian motions predictable?

We provide a device, called the local predictor, which extends the idea of the predictable compensator. It is shown that a fBm with the Hurst index greater than 1/2 coincides with its local predictor while fBm with the Hurst index smaller than 1/2 does not admit any local predictor. Mathematics Subject Classification (2000). Primary 60G07; Secondary 60G15, 60G48, 60G25.