Exact bounds for tail probabilities of martingales with bounded differences

We consider random walks, say Wn = {0, M1, . . ., Mn} of length n starting at 0 and based on a martingale sequence Mk = X1 + ··· + Xk with differences Xm. Assuming |Xk| \leq 1 we solve the isoperimetric problem Bn(x) = supP\{Wn visits an interval [x,∞)\},  (1) where sup is taken over all poss...

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Bibliographic Details
Main Author: Dainius Dzindzalieta
Format: Article
Language:English
Published: Vilnius University Press 2009-12-01
Series:Lietuvos Matematikos Rinkinys
Subjects:
Online Access:https://www.journals.vu.lt/LMR/article/view/18001