The von Mises–Fisher distribution of the first exit point from the hypersphere of the drifted Brownian motion and the density of the first exit time

2013 ◽  
Vol 83 (7) ◽  
pp. 1669-1676 ◽  
Author(s):  
Riccardo Gatto
Keyword(s):  
Brownian Motion ◽  
Exit Time ◽  
Exit Point ◽  
First Exit Time ◽  
Fisher Distribution ◽  
Von Mises

scholarly journals On the Distribution of First Exit Time for Brownian Motion with Double Linear Time-Dependent Barriers

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Lin Xu ◽  
Dongjin Zhu
Keyword(s):  
Brownian Motion ◽  
Linear Time ◽  
Exit Time ◽  
Time Dependent ◽  
First Exit Time ◽  
Main Method ◽  
Analytical Expression ◽  
Finite Series ◽  
Girsanov Transform ◽  
Linear Barrier

This paper focuses on the first exit time for a Brownian motion with a double linear time-dependent barrier specified by y=a+bt, y=ct, (a>0, b<0, c>0). We are concerned in this paper with the distribution of the Brownian motion hitting the upper barrier before hitting the lower linear barrier. The main method we applied here is the Girsanov transform formula. As a result, we expressed the density of such exit time in terms of a finite series. This result principally provides us an analytical expression for the distribution of the aforementioned exit time and an easy way to compute the distribution of first exit time numerically.

scholarly journals AN INTEGRAL EQUATION FOR THE DISTRIBUTION OF THE FIRST EXIT TIME OF A REFLECTED BROWNIAN MOTION

2009 ◽  
Vol 50 (4) ◽  
pp. 445-454 ◽  
Author(s):  
VICTOR DE-LA-PEÑA ◽  
GERARDO HERNÁNDEZ-DEL-VALLE ◽  
CARLOS G. PACHECO-GONZÁLEZ
Keyword(s):  
Integral Equation ◽  
Brownian Motion ◽  
First Passage Time ◽  
Exit Time ◽  
Numerical Procedure ◽  
Passage Time ◽  
Reflected Brownian Motion ◽  
First Exit Time ◽  
Time Problem ◽  
First Passage Time Problem

AbstractReflected Brownian motion is used in areas such as physiology, electrochemistry and nuclear magnetic resonance. We study the first-passage-time problem of this process which is relevant in applications; specifically, we find a Volterra integral equation for the distribution of the first time that a reflected Brownian motion reaches a nondecreasing barrier. Additionally, we note how a numerical procedure can be used to solve the integral equation.

scholarly journals Upper and lower bounds of the first exit time of Brownian motion from The Minimum and Maximun Parabolic Domains with variable dimension to research the variation of biological species

2020 ◽  
Author(s):  
Chao Liu ◽  
Wenbin Che ◽  
Jingjun Zhang
Keyword(s):  
Brownian Motion ◽  
Lower Bounds ◽  
Exit Time ◽  
Biological Species ◽  
Integral Function ◽  
Upper And Lower Bounds ◽  
First Exit Time ◽  
Variable Dimension ◽  
First Time ◽  
Exact Constants

Abstract Consider a Brownian motion with variable dimension starting at an interior point of the minimum or maximum parabolic domains Dmax t and Dmin t in Rd(t)+2, d(t) ≥ 1 is an increasing integral function as t →∞,d(t) →∞, and let τDmax t and τDmin t denote the first time the Brownian motion exits from Dmax t and Dmin t , respectively. Upper and lower bounds with exact constants for the asymptotics of logP(τDmax t > t) and logP(τDmin t > t) are given as t → ∞, depending on the shape of the domain Dmax t and Dmin t . The methods of proof are based on Gordon’s inequality and early works of Li, Lifshits and Shi in the single general parabolic domain case.

An integral equation for the distribution of the first exit time of a reflected Brownian motion

2009 ◽  
Vol 50 ◽  
Author(s):  
Victor De-la-Peña ◽  
Gerardo Hernandez-del-Valle ◽  
Carlos Gabriel Pacheco-Gonzalez
Keyword(s):  
Integral Equation ◽  
Brownian Motion ◽  
Exit Time ◽  
Reflected Brownian Motion ◽  
First Exit Time
Sign in / Sign up

Export Citation Format

Share Document