Large deviations: An introduction to 2007 Abel prize

DOI10.1007/s12044-008-0009-5zbMath1146.60023OpenAlexW1968116256MaRDI QIDQ943020

B. E. Eshmatov

Publication date: 8 September 2008

Published in: Proceedings of the Indian Academy of Sciences. Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12044-008-0009-5

zbMATH Keywords

Hamilton-Jacobi equationMarkov processesergodicityWentzell-Freidlin theoryprincipal eigenvaluerate functionFeynman-Kac formulaoccupation timeempirical distributionBurger's equationSanov's theoremexit problemLaplace's methodCramer's theoremlarge deviation principle (LDP)variational formulaweak convergence of probability measuresVaradhan's lemmaconvex conjugatesBrownian motion/diffusionDonsker-Varadhan theoryEsscher transform/tiltsample path LDP

Mathematics Subject Classification ID

Large deviations (60F10)

Related Items (2)

General theorems on large deviations for random vectors ⋮ Large deviations for Lévy diffusions in the small noise regime

Cites Work

• Large deviation properties of data streams that share a buffer
• Large deviations and queueing networks: Methods for rate function identification
• A time-reversed representation for the tail probabilities of stationary reflected Brownian motion.
• Asymptotic evaluation of certain markov process expectations for large time. IV
• On Large Deviations from the Invariant Measure
• Asymptotic probabilities and differential equations
• General analogues to the law of the iterated logarithm
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