p. 113 - 118 Convergence of the Increments of a Wiener Process A. Bahram Received: March 4, 2013; Accepted: August 26, 2013 Abstract. Let \lambda(tt,\alpha) = (2at (log(t/at) + \alpha log log t + (1-\alpha) log log at))-1/2 where 0 <= \alpha <= 1 and W(t) be a standard Wiener process. Suppose that at is a nondecreasing function of t such that 0 < at <= t and at /t is nonincreasing. In this paper we study the almost sure behaviour of limsup(k \to \infty)sup0 <= s <= at_{k} \lambda(tk,\alpha)|W(tk + s) - W(tk)| where {tk} be some increasing sequence diverging to \infty. Keywords: Wiener process; increments of a Wiener process; law of the iterated logarithm; Strong approximations. AMS Subject classification: Primary: 60F15, 60G17, 68R10 PDF Compressed Postscript Version to read ISSN 0862-9544 (Printed edition) Faculty of Mathematics, Physics and Informatics Comenius University 842 48 Bratislava, Slovak Republic Telephone: + 421-2-60295111 Fax: + 421-2-65425882 e-Mail: amuc@fmph.uniba.sk Internet: www.iam.fmph.uniba.sk/amuc © 2014, ACTA MATHEMATICA UNIVERSITATIS COMENIANAE |