Moment and tail estimates for martingales and martingale transform, with application to the martingale limit theorem in Banach spaces
arXiv:1206.4964
Abstract
In this paper non-asymptotic exponential and moment estimates are derived for tail of distribution for discrete time martingale and martingale transform by means of martingale differences in the terms of moments and tails of distributions of summands and multipliers. We show also the exactness of obtained estimations and consider some applications in the theory of limit theorem for Banach space valued martingales.
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- Sharp moment estimates for polynomial martingales
- Central Limit Theorem and exponential tail estimations in mixed (anisotropic) Lebesgue spaces
- Central limit theorem and exponential tail estimations in hybrid Lebesgue-continuous spaces
- Tail estimates for martingale under "LLN" norming sequence
- Exact exponential tail estimations in the Law of Iterated Logarithm for Bochner's mixed Lebesgue spaces
- Random processes and Central Limit Theorem in Besov spaces