Occupation times of balls by Brownian motion with drift

Chuancun Yin; Sung Nok CHIU

doi:10.1142/S0252959901000061 [not accessible, 2023-09-20]

Occupation times of balls by Brownian motion with drift

Chuancun Yin^*, Sung Nok CHIU

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

Abstract

Let X = {X_t, t ≥ 0} be a d-dimensional (d ≥ 2) standard Brownian motion with drift c started at a fixed x, and B_R = {x ∈ ℝ^d : \x\ < R}, the ball centered at 0 with radius R. Consider the distributions of T_R(t) and T_R(∞), where T_R(t) denotes the time spent by X in B_R up to time t and T_R(∞) the total time of X spent in B_R. Explicit formulas for the Laplace transform of T_R(∞) and the double Laplace transform of T_R(t) are obtained.

Original language	English
Pages (from-to)	47-56
Number of pages	10
Journal	Chinese Annals of Mathematics. Series B
Volume	22
Issue number	1
DOIs	https://doi.org/10.1142/S0252959901000061 [not accessible, 2023-09-20]
Publication status	Published - 2001

Scopus Subject Areas

Mathematics(all)
Applied Mathematics

User-Defined Keywords

Ball
Brownian motion with drift
Laplace transform
Occupation time

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10.1142/S0252959901000061 [not accessible, 2023-09-20]

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title = "Occupation times of balls by Brownian motion with drift",

abstract = "Let X = {Xt, t ≥ 0} be a d-dimensional (d ≥ 2) standard Brownian motion with drift c started at a fixed x, and BR = {x ∈ ℝd : \x\ < R}, the ball centered at 0 with radius R. Consider the distributions of TR(t) and TR(∞), where TR(t) denotes the time spent by X in BR up to time t and TR(∞) the total time of X spent in BR. Explicit formulas for the Laplace transform of TR(∞) and the double Laplace transform of TR(t) are obtained.",

keywords = "Ball, Brownian motion with drift, Laplace transform, Occupation time",

author = "Chuancun Yin and CHIU, {Sung Nok}",

year = "2001",

doi = "10.1142/S0252959901000061 [not accessible, 2023-09-20]",

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TY - JOUR

T1 - Occupation times of balls by Brownian motion with drift

AU - Yin, Chuancun

AU - CHIU, Sung Nok

PY - 2001

Y1 - 2001

N2 - Let X = {Xt, t ≥ 0} be a d-dimensional (d ≥ 2) standard Brownian motion with drift c started at a fixed x, and BR = {x ∈ ℝd : \x\ < R}, the ball centered at 0 with radius R. Consider the distributions of TR(t) and TR(∞), where TR(t) denotes the time spent by X in BR up to time t and TR(∞) the total time of X spent in BR. Explicit formulas for the Laplace transform of TR(∞) and the double Laplace transform of TR(t) are obtained.

AB - Let X = {Xt, t ≥ 0} be a d-dimensional (d ≥ 2) standard Brownian motion with drift c started at a fixed x, and BR = {x ∈ ℝd : \x\ < R}, the ball centered at 0 with radius R. Consider the distributions of TR(t) and TR(∞), where TR(t) denotes the time spent by X in BR up to time t and TR(∞) the total time of X spent in BR. Explicit formulas for the Laplace transform of TR(∞) and the double Laplace transform of TR(t) are obtained.

KW - Ball

KW - Brownian motion with drift

KW - Laplace transform

KW - Occupation time

UR - http://www.scopus.com/inward/record.url?scp=25644445354&partnerID=8YFLogxK

U2 - 10.1142/S0252959901000061 [not accessible, 2023-09-20]

DO - 10.1142/S0252959901000061 [not accessible, 2023-09-20]

M3 - Journal article

AN - SCOPUS:25644445354

SN - 0252-9599

VL - 22

SP - 47

EP - 56

JO - Chinese Annals of Mathematics. Series B

JF - Chinese Annals of Mathematics. Series B

IS - 1

ER -

Occupation times of balls by Brownian motion with drift

Abstract

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