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On the Theory of Large Deviations
Theory of Probability & Its Applications, 1994Summary: The similarity of the ``large deviation principle, (DV1) and (DV2)'' and the ``weak convergence of probability measures'' was used by the author in the earlier paper [in: New trends in probability and statistics. Vol. 1, Proc. 23rd Bakuriani Colloq. in Honour of Yu. V.
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2017
This chapter applies Wentzell’s theory of large deviation s to the Wright–Fisher model, using the approach of Papangelou (Athens conference on applied probability and time series analysis. Lecture notes in statistics, vol 114. Springer, New York, pp 245–252, 1996; Papangelou, Ann Appl Probab, 8(1):182–192, 1998; Papangelou, Stochastic processes and ...
Julian Hofrichter +2 more
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This chapter applies Wentzell’s theory of large deviation s to the Wright–Fisher model, using the approach of Papangelou (Athens conference on applied probability and time series analysis. Lecture notes in statistics, vol 114. Springer, New York, pp 245–252, 1996; Papangelou, Ann Appl Probab, 8(1):182–192, 1998; Papangelou, Stochastic processes and ...
Julian Hofrichter +2 more
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An introduction to the theory of large deviations
Metrika, 1986As the title says, this is an introduction to the theory of large deviations. It provides an expository survey of classical results (Cramér's theorem, large deviation for Brownian motion, Strassen's functional iterated logarithm law) and the general setting of large deviation problems.
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Large deviation theory for coin tossing and turbulence
Physical Review E, 2009Large deviations play a significant role in many branches of nonequilibrium statistical physics. They are difficult to handle because their effects, though small, are not amenable to perturbation theory. Even the Gaussian model, which is the usual initial step for most perturbation theories, fails to be a starting point while discussing intermittency ...
Chakraborty, Sagar +2 more
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2000
Large deviation theory has deep historic roots, but its strong flowering in recent years has come about partly because of an increased appreciation of the beauty of the theory and of the many ways in which it can be viewed, but even more because of the realisation that it provides the natural tool in so many applications. Roughly, it applies to systems
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Large deviation theory has deep historic roots, but its strong flowering in recent years has come about partly because of an increased appreciation of the beauty of the theory and of the many ways in which it can be viewed, but even more because of the realisation that it provides the natural tool in so many applications. Roughly, it applies to systems
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An introduction to Large Deviations Theory
Στη Θεωρία Πιθανοτήτων είναι συνηθισμένο να παρατηρούμε συγκέντρωση της κατανομής τυχαίων μεταβλητών ...Loulakis, Michail +1 more
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Large Deviations in Ergodic Theory
1986The classical example of a large deviation result is Cramer’s theorem. It tells us, in a contemporary formulation, that if Y1, Y2,… is a sequence of independent real valued random variables with identical distribution function F such that $$ f(\theta ) = E[\exp \{ \theta Y_1 \} [ = \smallint \exp \{ \theta y\} F(dy)$$ is finite for all finite θ ...
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A large deviation theory analysis on the implicit bias of SGD
NeurocomputingStochastic Gradient Descent (SGD) plays a key role in training deep learning models, yet its ability to implicitly regularize and enhance generalization remains an open theoretical question. In this work, we explore the use of Large Deviation Theory (LDT) to explain why SGD selects models with strong generalization properties.
Luis A. Ortega 0001, Andrés R. Masegosa
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Two examples in the theory of large deviations
Statistics & Probability Letters, 1993Examples are given showing that the exponential compactness and the strict convexity of the Fenchel transform are both essential for having large deviations principle [in the form as it is, for instance, given in the book of \textit{J.-D. Deuschel} and \textit{D. W. Stroock}, Large deviations (1989; Zbl 0705.60029)].
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Large deviations in information theory and statistics
Proceedings of 1994 Workshop on Information Theory and Statistics, 2002Large deviations theory, a branch of probability theory that deals with estimates of probabilities of very rare events has close links with topics in information theory and in statistics. Some of these connections are explored.
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