Asymptotic approximations for Brownian motion boundary hitting times. (English) Zbl 0739.60074

Roberts, G. O.

Ann. Probab. 19, No. 4, 1689-1731 (1991).

From the author’s summary: “The problem of approximating boundary hitting times for diffusion processes, and in particular Brownian motion, is considered. Using a combination of probabilistic and function-analytic techniques, approximations for conditioned diffusion distributions are obtained. These lead to approximations for the distributions of the hitting time itself. The approximations are split into three cases depending on whether the boundary is upper case, approximation square root or lower case, and one-sided boundaries are also considered separately.”
The work depends on long computations involving several properties of special functions, so that more precise statements cannot be given here, and the reader is referred to the paper for details.

Reviewer: M.M.Rao (Riverside)

MSC:

60J65	Brownian motion
60J50	Boundary theory for Markov processes

Keywords:

approximate square-root boundaries; upper and lower case boundaries; hitting times for diffusion processes; properties of special functions