Exponential Bounds in the Law of Iterated Logarithm for Martingales
E. Ostrovsky, L.Sirota
TL;DR
This paper derives non-asymptotic exponential bounds for the tail distribution of maximum martingales, extending classical results related to the Law of Iterated Logarithm in a natural norming framework.
Contribution
It introduces new exponential estimates for martingale tails that align with the classical Law of Iterated Logarithm, providing sharper non-asymptotic bounds.
Findings
Derived exponential tail bounds for martingales
Extended classical LIL results to non-asymptotic setting
Applicable to Banach spaces of random variables
Abstract
In this paper non-asymptotic exponential estimates are derived for tail of maximum martingale distribution by naturally norming in the spirit of the classical Law of Iterated Logarithm. Key words: Martingales, exponential estimations, moment, Banach spaces of random variables, tail of distribution, conditional expectation.
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Taxonomy
TopicsAnalysis of environmental and stochastic processes · Mathematical Approximation and Integration · Stochastic processes and financial applications