On the large values of the Wiener process

Endre Csáki and Karl Grill

Stochastic Processes and their Applications, 1987, vol. 27, 43-56

Abstract: Let (W(t), t[greater-or-equal, slanted]0), be a standard Wiener process and define - M+ (t) = max{W(u): u[less-than-or-equals, slant]t},- M-(t) = max{-W(u): u[less-than-or-equals, slant]t},- Z(t) = max{u [less-than-or-equals, slant] t: W(u) = 0}. We investigate the asymptotic behaviour of Z(t) and M-(t) under the condition that M+(t) (or, equivalently, W(t)) gets very large, i.e. as large as indicated by the law of iterated logarithm.

Keywords: Wiener; process; strong; laws; law; of; iterated; logarithm; strong; approximation; partial; sum; process (search for similar items in EconPapers)
Date: 1987
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