G. O. Roberts. Asymptotic approximations for Brownian motion boundary hitting times. Annals of Probability, 19:1689--1731, 1991.

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Probability Approximations via the Poisson Clumping Heuristic: An .. - Aldous (1992)   (73 citations)  (Correct)

....pointed out that my discussion here is a little casual. Bramson and Durrett [15] construct analogous discrete space models which in any dimension exhibit the phase transition from subdiffusive to diffusive behavior which was claimed in my example. D33 Brownian motion boundary crossing. Roberts [43] gives formalizations of the heuristic for Brownian motion hitting a square root like boundary, via the transformation to the Ornstein Uhlenbeck process. D38 Berman s method. Albin [3] gives another formalization of the ergodic exit method, using discrete approximations, and emphasizing ....

G. O. Roberts. Asymptotic approximations for Brownian motion boundary hitting times. Annals of Probability, 19:1689--1731, 1991.

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