Results 1  10
of
25
Rates of convergence of diffusions with drifted Brownian potentials
 TRANS. AMER. MATH. SOC
, 1999
"... We are interested in the asymptotic behaviour of a diffusion process with drifted Brownian potential. The model is a continuous time analogue to the random walk in random environment studied in the classical paper of Kesten, Kozlov, and Spitzer. We not only recover the convergence of the diffusion ..."
Abstract

Cited by 20 (5 self)
 Add to MetaCart
We are interested in the asymptotic behaviour of a diffusion process with drifted Brownian potential. The model is a continuous time analogue to the random walk in random environment studied in the classical paper of Kesten, Kozlov, and Spitzer. We not only recover the convergence of the diffusion process which was previously established by Kawazu and Tanaka, but also obtain all the possible convergence rates. An interesting feature of our approach is that it shows a clear relationship between drifted Brownian potentials and Bessel processes.
A Vervaatlike path transformation for the reflected Brownian bridge conditioned on its local time at 0
, 1999
"... We describe a Vervaatlike path transformation for the reflected Brownian bridge conditioned on its local time at 0: up to random shifts, this process equals the two processes constructed from a Brownian bridge and a Brownian excursion by adding a drift and then taking the excursions over the cur ..."
Abstract

Cited by 13 (2 self)
 Add to MetaCart
We describe a Vervaatlike path transformation for the reflected Brownian bridge conditioned on its local time at 0: up to random shifts, this process equals the two processes constructed from a Brownian bridge and a Brownian excursion by adding a drift and then taking the excursions over the current minimum. As a consequence, these three processes have the same occupation measure, which is easily found. The three processes arise as limits, in three different ways, of profiles associated to hashing with linear probing, or, equivalently, to parking functions.
Hitting, Occupation, and Inverse Local Times of OneDimensional Diffusions: Martingale and Excursion Approaches
, 2001
"... Basic relations between the distributions of hitting, occupation, and inverse local times of a onedimensional diffusion process X , first discussed by ItoMcKean, are reviewed from the perspectives of martingale calculus and excursion theory. These relations, and the technique of conditioning o ..."
Abstract

Cited by 12 (1 self)
 Add to MetaCart
Basic relations between the distributions of hitting, occupation, and inverse local times of a onedimensional diffusion process X , first discussed by ItoMcKean, are reviewed from the perspectives of martingale calculus and excursion theory. These relations, and the technique of conditioning on L y T , the local time of X at level y before a suitable random time T , yield formulae for the joint Laplace transform of L y T and the times spent by X above and below level y up to time T.
Simulation of a stochastic process in a discontinuous, layered media
, 2011
"... In this note, we provide a simulation algorithm for a diffusion process in a layered media. Our main tools are the properties of the Skew Brownian motion and a path decomposition technique for simulating occupation times. ..."
Abstract

Cited by 7 (4 self)
 Add to MetaCart
(Show Context)
In this note, we provide a simulation algorithm for a diffusion process in a layered media. Our main tools are the properties of the Skew Brownian motion and a path decomposition technique for simulating occupation times.
Constructions Of A Brownian Pathwith A Given Minimum
, 1999
"... We construct a Brownian path conditioned on its minimum value over a fixed time interval by simple transformations of a Brownian bridge. Path transformations have proved useful in the study of Brownian motion and related processes, by providing simple constructions of various conditioned processes ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
We construct a Brownian path conditioned on its minimum value over a fixed time interval by simple transformations of a Brownian bridge. Path transformations have proved useful in the study of Brownian motion and related processes, by providing simple constructions of various conditioned processes such as Brownian bridge, meander and excursion, starting from an unconditioned Brownian motion. As well as providing insight into the structure of these conditioned processes, path constructions assist in the computation of various conditional laws of Brownian functionals, and in the simulation of conditioned processes. Starting from a standard onedimensional Brownian motion B =(B t ) 0#t#1 with B 0 =0, one well known construction of a Brownian bridge of length 1 from 0 to x, denoted B br,x ,is the following: B br,x u := B u  uB 1 + ux (0 # u # 1). (1) Then a Brownian meander of length 1 starting at 0 and conditioned to end at r # 0, denoted B me,r , can be constructed from...
Large Favourite Sites Of Simple Random Walk And The Wiener Process
 Electronic J. Probab
, 1998
"... Let U(n) denote the most visited point by a simple symmetric random walk fS k g k0 in the first n steps. It is known that U(n) and max 0kn S k satisfy the same law of the iterated logarithm, but have different upper functions (in the sense of P. Lévy). The distance between them however turns out to ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
Let U(n) denote the most visited point by a simple symmetric random walk fS k g k0 in the first n steps. It is known that U(n) and max 0kn S k satisfy the same law of the iterated logarithm, but have different upper functions (in the sense of P. Lévy). The distance between them however turns out to be transient. In this paper, we establish the exact rate of escape of this distance. The corresponding problem for the Wiener process is also studied.
The maximum of the local time of a diffusion process in a drifted Brownian potential
, 2006
"... ..."
THE ARCSINE LAW AS THE LIMIT OF THE INTERNAL DLA CLUSTER GENERATED BY SINAI’S WALK
, 903
"... Abstract. We identify the limit of the internal DLA cluster generated by Sinai’s walk as the law of a functional of a Brownian motion which turns out to be a new interpretation of the Arcsine law. Keywords: Sinai’s walk, internal DLA, random walks in random environments, excursion theory. 1. ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
(Show Context)
Abstract. We identify the limit of the internal DLA cluster generated by Sinai’s walk as the law of a functional of a Brownian motion which turns out to be a new interpretation of the Arcsine law. Keywords: Sinai’s walk, internal DLA, random walks in random environments, excursion theory. 1.