Sharp Ratio Inequalities for a Conditionally Symmetric Martingale
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: Bulletin of the Polish Academy of Sciences Mathematics
سال: 2010
ISSN: 0239-7269,1732-8985
DOI: 10.4064/ba58-1-8