Sharp maximal inequalities for conditionally symmetric martingales and Brownian motion
نویسندگان
چکیده
منابع مشابه
Sharp Maximal Inequalities for Conditionally Symmetric Martingales and Brownian Motion
Let B = {Bt)t>0 be a standard Brownian motion. For c > 0, k > 0 , let T(c, k) = inî{t > 0: maxs<í Bs cBt > k} , T"(c,k)= inf{r>0: max^, \BS\ c\B,\ > k} . We show that for c > 0 and k > 0, both T(c, k) and T*{c, k) axe finite almost everywhere. Moreover, T(c, k) and T*(c, k) e L if and only if c < pKp 1) for p > 1 , and for all c > 0 when p < 1 . These results have analogues for simple random wa...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1991
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1991-1059638-8