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Some boundary-crossing results for linear diffusion processes

✍ Scribed by Changsun Choi; Dougu Nam

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
228 KB
Volume
62
Category
Article
ISSN
0167-7152

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✦ Synopsis

We evaluate some boundary-crossing time density functions for time-changed Brownian motion. As examples, we evaluate the ΓΏrst passage time densities of Ornstein-Uhlenbeck process to exponential boundaries and Brownian bridge to two linearly shrinking boundaries. We also evaluate explicitly the ΓΏrst and last passage time distributions of Brownian motion for two linear boundaries.

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Explicit formulae are found for the probability that the Brownian motion, B t ; up-crosses, in [0; T ]; a piecewise-linear function S(t); with the condition that the value of B t is assigned at a future time u ΒΏ T or at an intermediate time u Β‘ T . Also, the analogous conditional probability concern