ACTA MATHEMATICA UNIVERSITATIS COMENIANAE

ACTA MATHEMATICA UNIVERSITATIS COMENIANAE

Vol. LXXIV, 2 (2005)
p. 163 - 168

Some Results on Increments of the Wiener Process
A. Bahram

Abstract. Let l _{( T,a_T
,a
)} =

^-1/2 where 0 < a < 1 and {W (t), t > 0} be a standard Wiener process. This paper studies the almost sure limiting behaviour of sup_{0<t<T-a_T} l _{( T,a_T
,a
)} |W(t + a_T) – W(t)| as T ® ¥ under varying conditions on a_T and T/a_T .

Keywords: Wiener process, increments of a Wiener process, a law of the iterated logarithm.

AMS Subject classification: 60J65.

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Acta Mathematica Universitatis Comenianae
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