Probabilistic estimates of large deviations of sums of independent random variables and martingales. (English. Russian original) Zbl 0746.60047

Matsak, I. K.

Theory Probab. Math. Stat. 42, 103-111 (1991); translation from Teor. Veroyatn. Mat. Stat., Kiev 42, 88-95 (1990).

Let \(M_ n\) be a martingale, \(M_ 0=0\). Estimates for \(P(M_ n>xn^{1/2})\) are given, sharpening previously known results. The inequality is then applied to the norm of the sum of independent Banach space valued random variables.

Reviewer: W.Bryc (Cincinnati)

MSC:

60G42	Martingales with discrete parameter
60F10	Large deviations
60E15	Inequalities; stochastic orderings
60G50	Sums of independent random variables; random walks

Keywords:

inequalities for large deviations of martingales; Banach space valued random variables