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| OCCUPATION TIMES OF BALLS BY BROWNIAN MOTION WITH DRIFT |
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Citation： |
YIN Chuancun,CHIU Sungnok.OCCUPATION TIMES OF BALLS BY BROWNIAN MOTION WITH DRIFT[J].Chinese Annals of Mathematics B,2001,22(1):47~56 |
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Net amount： 1111 |
Authors： |
YIN Chuancun; CHIU Sungnok |
Foundation： |
Project supported by the National Natural Science Foundation of China (No.19801020) and the grant from the Research Grants Council of the Hong Kong special Administrative Region, China(No.HKBU/2075/98p). |
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| Abstract： |
Let $X = {X_t, t \geq 0}$ be a d-dimensional (d \geq 2) standard Brownian motion with drift c started at a fixed x, and $B_R = {x \in R^d : \|x\| < R}$, the ball centered at 0 with radius R. Consider the distributions of $T_R(t)$ and $T_R(\infty)$, where $T_R(t)$ denotes the time spent by X in $B_R$ up to time t and $T_R(\infty)$ the total time of X spent in $B_R$. Explicit formulas for the Laplace transform of $T_R(\infty)$ and the double Laplace transform of $T_R(t)$ are obtained. |
Keywords： |
Brownian motion with drift, Occupation time, Ball, Laplace transform |
Classification： |
60J65 |
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