Tail estimates for martingale under "LLN" norming sequence

2012/07/08 by E. Ostrovsky, Ostrovsky, E., L. Sirota +1
Decision Sciences · Mathematics · #Advanced Harmonic Analysis Research #FOS: Mathematics #Mathematical Approximation and Integration #Probability (math.PR) #Probability and Risk Models #math.PR

paper · pdf · doi:10.48550/arxiv.1207.1908

arxiv created 2012/07/08 · openalex publication_date 2012/07/08 · arxiv updated 2012/07/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper non-asymptotic exponential and moment estimates are derived for tail of distribution for discrete time martingale under norming sequence 1/n, as in the classical Law of Large Numbers (LLN), by means of martingale differences as a rule in the terms of unconditional moments and tails of distributions of summands. We show also the exactness of obtained estimations.

Citations

• Non-Improved Uniform Tail Estimates for Normed Sums of Independent Random Variables with Heavy Tails, with applications

Related

• Moment and tail estimates for martingales and martingale transform, with application to the martingale limit theorem in Banach spaces
• Exponential Bounds in the Law of Iterated Logarithm for Martingales
• Sharp moment estimates for polynomial martingales
• Moment and exponential estimation for the distribution of the norms for random matrices martingales
• Bide - Side Exponential and Moment Inequalities for Tails of Distributions of Polynomial Martingales