| Title |
An exact bound for tail probabilities for a class of conditionally symmetric bounded martingales / |
| Translation of Title |
Tikslus rėžis sąlyginai aprėžtų martingalų klasės uodegų tikimybėms. |
| Authors |
Dzindzalieta, Dainius |
| DOI |
10.15388/LMR.2006.30792 |
| Full Text |
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| Is Part of |
Lietuvos matematikos rinkinys. 2006, T. 46, spec, Nr, p. 433-438.. ISSN 0132-2818 |
| Keywords [eng] |
Probability, tail ; Martingales ; Random walk ; Isoperimetric |
| Abstract [eng] |
We consider the class, say M_n,sym, of martingales M_n = X_1 + ... + X_n with conditionally symmetric bounded differences X_k such that |X_k|<=1. We find explicitly a solution, say D_n(x), of the variational problem [...]. We show that this problem is equivalent to one when you want to find out the symmetric random walk with bounded length of steps which maximizes the probability to visit an interval [x; ∞]. The function x->D_n(x) allows a simple description and is closely related to the binomial tail probabilities. We can interpret the result as a final and optimal upper bound P{M_n>=x} <= D_n(x), x € R, for the tail probability P{M_n>=x}. |
| Type |
Journal article |
| Language |
English |
| Publication date |
2006 |
| CC license |
|
