On the maximum of a Wiener process and its location
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Summary
Consider a Wiener process {W(t),t≧0}, letM(t)=max |W(s)| andv(t) be the location of the maximum of the absolute value of\(\mathop {W( \cdot )}\limits^{ 0\mathop< \limits_ = s\mathop< \limits_ = t} \) in [0,t] i.e.|W(v(t))|=M(t). We study the limit points of (α t M(t),β t v(t)) ast→∞ where α t and β t are positive, decreasing normalizing constants. Moreover, a lim inf result is proved for the length of the longest flat interval ofM(t).
Keywords
Stochastic Process Probability Theory Mathematical Biology Limit Point Wiener Process
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