Relations between exponential tails, moments and moment generating functions for random variables and vectors
Yu.V. Kozachenko, E. Ostrovsky, L. Sirota
TL;DR
This paper establishes precise, non-asymptotic relationships between tail decay, moments, and moment generating functions for random variables and vectors, enhancing understanding of their interdependence.
Contribution
It introduces exact, non-asymptotic relations linking tail behavior, moments, and moment generating functions for random variables and vectors.
Findings
Exact relations between tail decay and moments
Connections between moments and moment generating functions
Non-asymptotic bounds for random variables and vectors
Abstract
We offer in this paper the non-asymptotical pairwise bilateral exact up to multiplicative constants interrelations between exponential decreasing tail behavior, moments (Grand Lebesgue Spaces) norm and moment generating functions norm for random variables and vectors (r.v.).
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Taxonomy
TopicsProbability and Risk Models · Mathematical Approximation and Integration · Financial Risk and Volatility Modeling