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008			100301s2010 gw | s |||| 0|eng d
020			_a9783642033117 _9978-3-642-03311-7
082			_a003 _223
100			_aDembo, Amir. _920100
245			_aLarge Deviations Techniques and Applications _h[electronic resource] / _cby Amir Dembo, Ofer Zeitouni.
250			_a2nd ed. 2010.
260			_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg : _bImprint: Springer, _c2010.
300			_aXVI, 396 p. _bonline resource.
505			_aLDP for Finite Dimensional Spaces -- Applications-The Finite Dimensional Case -- General Principles -- Sample Path Large Deviations -- The LDP for Abstract Empirical Measures -- Applications of Empirical Measures LDP.
520			_aThe theory of large deviations deals with the evaluation, for a family of probability measures parameterized by a real valued variable, of the probabilities of events which decay exponentially in the parameter. Originally developed in the context of statistical mechanics and of (random) dynamical systems, it proved to be a powerful tool in the analysis of systems where the combined effects of random perturbations lead to a behavior significantly different from the noiseless case. The volume complements the central elements of this theory with selected applications in communication and control systems, bio-molecular sequence analysis, hypothesis testing problems in statistics, and the Gibbs conditioning principle in statistical mechanics. Starting with the definition of the large deviation principle (LDP), the authors provide an overview of large deviation theorems in ${{\rm I\!R}}^d$ followed by their application. In a more abstract setup where the underlying variables take values in a topological space, the authors provide a collection of methods aimed at establishing the LDP, such as transformations of the LDP, relations between the LDP and Laplace's method for the evaluation for exponential integrals, properties of the LDP in topological vector spaces, and the behavior of the LDP under projective limits. They then turn to the study of the LDP for the sample paths of certain stochastic processes and the application of such LDP's to the problem of the exit of randomly perturbed solutions of differential equations from the domain of attraction of stable equilibria. They conclude with the LDP for the empirical measure of (discrete time) random processes: Sanov's theorem for the empirical measure of an i.i.d. sample, its extensions to Markov processes and mixing sequences and their application. The present soft cover edition is a corrected printing of the 1998 edition. Amir Dembo is a Professor of Mathematics and of Statistics at Stanford University. Ofer Zeitouni is a Professor of Mathematics at the Weizmann Institute of Science and at the University of Minnesota.
650			_aSystem theory. _920101
650			_aControl theory. _920102
650			_aProbabilities. _920103
650			_aSystems Theory, Control . _920104
650			_aProbability Theory. _920105
700			_aZeitouni, Ofer. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut _920106
856			_uhttps://doi.org/10.1007/978-3-642-03311-7
942			_cEBK
999			_c13603 _d13603