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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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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 Theory and Empirical Estimator Choice
2006Criterion choice is such a hard problem in information recovery and in estimation and inference. In the case of inverse problems with noise, can probabilistic laws provide a basis for empirical estimator choice? That is the problem we investigate in this paper.
Grendar, Marian +3 more
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Large Deviations Estimates in Semi‐Group Theory
AIP Conference Proceedings, 2008We translate in semi‐group theory our proof of Wentzel‐Freidlin estimates and our proof of Varadhan estimates for subelliptic Laplacians which was using the theory of large deviations of Wentzel‐Freidlin and the Malliavin Calculus of Bismut type.
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Application of large deviations in risk theory
2019In this paper we will explore how large deviation theory can be applied to risk measures and ruin theory. After giving a detailed introduction to large deviations and a short introduction to ruin theory and risk measures, we will analyse the application to a model with an insurer and a reinsurer, a risk measure model with mixed distributions and the ...
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A Brief Introduction to Large Deviations Theory
2012In this chapter we introduce the main concepts of large deviations theory. We state some of the main theorems with several examples, from Cramer theorem for the sum of independent random variables, to Freidlin–Wentzell theory of random perturbation of dynamical systems.
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