Asymptotic Comparisons of Functionals of Brownian Motion and Random Walk

In this paper we make comparisons involving stopping times $\tau$ of a process $X$ and the maximal function $X^\ast_\tau$ of that process, where $X$ is either Brownian motion or random walk. In particular, we give conditions implying that $P(X^\ast_\tau > \lambda) \approx P(\tau^{1/2} > \lambd...

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Veröffentlicht in:	The Annals of probability 1980-12, Vol.8 (6), p.1135-1147
1. Verfasser:	Kindermann, Ross P.
Format:	Artikel
Sprache:	eng
Schlagworte:	60G40 60J15 60J65 Brownian motion Integers Jumping martingale Martingales Mathematical inequalities Mathematical theorems maximal function Random walk Real numbers Stopping distances Stopping time
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