Central limit theorem and exponential tail estimations in hybrid Lebesgue-continuous spaces

2013/09/09 by E. Ostrovsky, Ostrovsky, E., L. Sirota +1
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #Advanced Harmonic Analysis Research #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1309.2344

openalex publication_date 2013/09/09 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We study the Central Limit Theorem (CLT) in the so-called hybrid Lebesgue-continuous spaces and tail behavior of normed sums of centered random independent variables (vectors) with values in these spaces.

Citations

• CLT for continuous random processes under approximations terms
• Schlomilch and Bell Series for Bessel's Functions, with Probabilistic Applications
• Maximal Inequalities in Bilateral Grand Lebesque Spaces Over Unbounded Measure
• Monte-Carlo method for multiple parametric integrals calculation and solving of linear integral Fredholm equations of a second kind, with confidence regions in uniform norm
• Central Limit Theorem and exponential tail estimations in mixed (anisotropic) Lebesgue spaces
• Asymptotic exponential bounds for MLE deviation under minimal conditions via classical and generic chaining methods
• Exact exponential bounds for the random field maximum distribution via the majoring measures (generic chaining)
• StrongL p -solutions of the Navier-Stokes equation inR m , with applications to weak solutions

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• Central Limit Theorem in Lebesgue-Riesz spaces for weakly dependent random sequences
• Random processes and Central Limit Theorem in Besov spaces