On Accuracy of Approximations for Wiener Probabilities to stay between square root boundaries
On accuracy of approximations for Wiener probabilities to stay between square root boundaries
Siberian Electronic Mathematical Reports, 22, 2, pp. 1614-1625 (2025)
Abstract:
Several asymptotic formulas for probabilities of the Wiener process to stay between different square root boundaries are known after papers of Breiman (1965), Sato (1977), Novikov (1979, 1981), Gärtner (1982), Uchiyama (1980), Greenwood and Perkins (1983). In the present work we investigate accuracy of these approximations. We present several general estimates in the
case of two boundaries. In particular, these estimates contain the ones obtained earlier by Uchiyama in the limiting case of one boundary.
Keywords: Brownian motion, Wiener process, square root boundaries, exit time, accuracy of approximation