Chebyshev-Type Exponential Inequalities for Sums of Random Vectors and for Trajectories of Random Walks

DOI10.1137/S0040585X97985182zbMath1238.60022OpenAlexW1990233169MaRDI QIDQ2882760

Aleksandr A. Borovkov, Anatoliĭ Alfredovich Mogul'skiĭ

Publication date: 7 May 2012

Published in: Theory of Probability & Its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/s0040585x97985182

zbMATH Keywords

large deviationslarge deviation principleconvex setaction functionalrandom walkCramér's conditiondeviation functionallarge deviation rate functionextended large deviation principleinequalities for large deviations

Mathematics Subject Classification ID

Inequalities; stochastic orderings (60E15) Sums of independent random variables; random walks (60G50)

Related Items (8)

Local theorems for arithmetic compound renewal processes when Cramer's condition holds ⋮ Inequalities and principles of large deviations for the trajectories of processes with independent increments ⋮ The extended large deviation principle for a process with independent increments ⋮ Exponential Chebyshev inequalities for random graphons and their applications ⋮ The large deviation principle for a compound Poisson process ⋮ Local theorems for finite-dimensional increments of compound multidimensional arithmetic renewal processes with light tails ⋮ On large deviation principles in metric spaces ⋮ Uniform rates of the Glivenko-Cantelli convergence and their use in approximating Bayesian inferences

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