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On the large values of the Wiener process

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.
Year of publication:
1987
Authors: Csáki, Endre ; Grill, Karl
Published in:
Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 27.1987, p. 43-56
Publisher: Elsevier
Keywords: Wiener process strong laws law of iterated logarithm strong approximation partial sum process
Type of publication: Article
Source:
Persistent link: https://www.econbiz.de/10008874787
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