On the maximum of a Wiener process and its location

Summary Consider a Wiener process {W(t),t0}, letM(t)=max |W(s)| andv(t) be the location of the maximum of the absolute value of in [0,t] i.e.|W(v(t))|=M(t). We study the limit points of (_tM(t),_tv(t)) ast where _t and _t are positive, decreasing normalizing constants. Moreover, a lim inf result is proved for the length of the longest flat interval ofM(t).Research supported by Hungarian National Foundation for Scientific Research Grant n. 1808