Approximate Exit Probabilities for a Brownian Bridge on a Short Time Interval, and Applications.
STANFORD UNIV CA DEPT OF STATISTICS
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Let T be the first exit time of Brownian motion Wt from a region R in d-dimensional Euclidean space having a smooth boundary. Given points xi sub o and xi sub 1 in R, ordinary and large deviation approximations are given for PrTxiW0 xi sub o, Wepsilon xi sub 1 as epsilon approaches limit of 0. Applications are given to hearing the shape of a drum, approximating the second virial coefficient, and Monte Carlo estimation of first passage distributions for Brownian motion.
- Statistics and Probability