Tail estimates for martingale under "LLN" norming sequence

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.

References in corpus (2)

• Exponential inequalities for martingales and asymptotic properties of the free energy of directed polymers in random environment
• Moment and tail estimates for martingales and martingale transform, with application to the martingale limit theorem in Banach spaces

Cited by in corpus (1)

• Tchebyshev's characteristic of rearrangement invariant space