Sharp moment estimates for polynomial martingales

Abstract

In this paper non-asymptotic moment estimates are derived for tail of distribution for discrete time polynomial martingale by means of martingale differences as a rule in the terms of unconditional and unconditional relative moments and tails of distributions of summands.We show also the exactness of obtained estimations.

Sharp moment and exponential tail estimates for U-statistics

“…for the polynomial martingales from appropriate independent random variables in [13], [18]. The case of arbitrary polynomial martingales was grounded in authors report [27].…”

“…There are many works about this problem; the next list is far from being complete: [3], [29], [12], [14], [19], [21], [27] etc. ; see also reference therein.…”

“…But in the recent publication about martingales [27] relaying in turn on the famous result belonging to A.Osekowski [22] the estimate(2.4) was improved:…”

“…It is proved in [27] in particular that the "constant" C 3 (d) in (2.4) allows the following simple estimate:…”

Sharp bounds for the spherical restriction Fourier transform in classical Lebesgue-Riesz and Grand Lebesgue spaces for ordinary and radial functions

“…Suppose now that the function f = f (x) belongs to sone GLS Gψ(a, b), ∃ψ ∈ Ψ : The non -improvability for this constant is grounded in particular in [27].…”