Banach spaces characterization of random vectors with exponential decreasing tails of distribution

2016/01/19 by E. Ostrovsky, Ostrovsky, E., L. Sirota +1
Mathematics · #FOS: Mathematics #Probability (math.PR) #math.PR

paper · pdf · doi:10.48550/arxiv.1601.04766

arXiv admin note: substantial text overlap with arXiv:1510.04182

arxiv created 2016/01/19 · arxiv updated 2016/01/20

Abstract

We present in this paper the Banach space representation for the set of random finite-dimensional vectors with exponential decreasing tails of distributions. We show that there are at last three types of these multidimensional Banach spaces, i.e. which can completely describe the random vectors with exponential decreasing tails of distributions: exponential Orlicz spaces, Young spaces and Grand Lebesgue spaces. We discuss in the last section the possible applications of obtained results.

Citations

• Vector rearrangement invariant banach spaces of random variables with exponential decreasing tails of distributions

Related

• Vector rearrangement invariant banach spaces of random variables with exponential decreasing tails of distributions
• Exact exponential tail estimations in the Law of Iterated Logarithm for Bochner's mixed Lebesgue spaces
• Non-asymptotical sharp exponential estimates for maximum distribution of discontinuous random fields
• Exact exponential tail estimation for sums of independent centered random variables, under natural norming, with applications to the theory of U-statistics
• Exponential Orlicz Spaces: New Norms and Applications