The principle of large deviations for almost everywhere central limit theorem

DOI10.1016/S0304-4149(98)00023-4zbMath0934.60022OpenAlexW2014147741MaRDI QIDQ1805776

Matthias K. Heck

Publication date: 18 November 1999

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0304-4149(98)00023-4

zbMATH Keywords

Brownian motioncentral limit theoremalmost sure invariance principleprinciple of large deviationsalmost everywhere central limit theorem

Mathematics Subject Classification ID

Strong limit theorems (60F15) Large deviations (60F10)

Related Items (11)

Large deviations for some logarithmic means in the case of random variables with thin tails ⋮ Asymptotic results for weighted means of linear combinations of independent Poisson random variables ⋮ Large deviation principles for sequences of logarithmically weighted means ⋮ Strong approximations for nonconventional sums and almost sure limit theorems ⋮ Non-asymptotic Gaussian estimates for the recursive approximation of the invariant distribution of a diffusion ⋮ On the large deviation principle for the almost sure CLT. ⋮ Asymptotic results for weighted means of random variables which converge to a Dickman distribution, and some number theoretical applications ⋮ Toward the history of the Saint St. Petersburg school of probability and statistics. I: Limit theorems for sums of independent random variables ⋮ Large deviations for weighted means of random vectors defined in terms of suitable Lévy processes ⋮ Large deviations and Wschebor's theorems ⋮ On large deviations for some sequences of weighted means of Gaussian processes

Cites Work

• A note on the almost sure central limit theorem
• A simultaneous almost everywhere central limit theorem for diffusions and its application to path energy and eigenvalues of the Laplacian
• The large deviation principle for hypermixing processes
• On large deviations of empirical measures for stationary Gaussian processes
• Asymptotic evaluation of certain markov process expectations for large time. IV
• On Strong Versions of the Central Limit Theorem
• An almost everywhere central limit theorem
• Asymptotic evaluation of certain markov process expectations for large time, I
• Asymptotic evaluation of certain markov process expectations for large time, II
• Asymptotic evaluation of certain Markov process expectations for large time—III
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