Sharp moment estimates for polynomial martingales

2014/10/03 by E. Ostrovsky, Ostrovsky, E., L. Sirota +1 · 4 citations
Economics, Econometrics and Finance · Mathematics · #Advanced Harmonic Analysis Research #FOS: Mathematics #Mathematical functions and polynomials #Probability (math.PR) #Stochastic processes and financial applications #math.PR

paper · pdf · doi:10.48550/arxiv.1410.0739

arxiv created 2014/10/03 · openalex publication_date 2014/10/03 · arxiv updated 2014/10/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Schlomilch and Bell Series for Bessel's Functions, with Probabilistic Applications
• Non-Improved Uniform Tail Estimates for Normed Sums of Independent Random Variables with Heavy Tails, with applications

Cited by

• Moment and tail estimates and Banach space valued Non-Central Limit Theorem (NCLT) for sums of multi-indexed random variables, processes and fields
• Equivalence between tails, Grand Lebesgue Spaces and Orlicz norms for random variables without Cramer's condition
• Uniform Limit Theorem and tail estimates for parametric u-statistics
• Bilateral tail estimate for distribution of self normalizes sums of independent centered random variables under natural norming

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