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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| Format: | Article |
| Language: | English |
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Vilnius University Press
2009-12-01
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| Series: | Lietuvos Matematikos Rinkinys |
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| Online Access: | https://www.journals.vu.lt/LMR/article/view/18001 |