000			03985nam a22004935i 4500
001			978-3-642-03311-7
003			DE-He213
005			20140220084525.0
007			cr nn 008mamaa
008			100301s2010 gw | s |||| 0|eng d
020			_a9783642033117 _9978-3-642-03311-7
024	7		_a10.1007/978-3-642-03311-7 _2doi
050		4	_aQ295
050		4	_aQA402.3-402.37
072		7	_aGPFC _2bicssc
072		7	_aSCI064000 _2bisacsh
072		7	_aTEC004000 _2bisacsh
082	0	4	_a519 _223
100	1		_aDembo, Amir. _eauthor.
245	1	0	_aLarge Deviations Techniques and Applications _h[electronic resource] / _cby Amir Dembo, Ofer Zeitouni.
264		1	_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg, _c2010.
300			_aXVI, 396p. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aStochastic Modelling and Applied Probability, _x0172-4568 ; _v38
505	0		_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		0	_aMathematics.
650		0	_aSystems theory.
650		0	_aDistribution (Probability theory).
650	1	4	_aMathematics.
650	2	4	_aSystems Theory, Control.
650	2	4	_aProbability Theory and Stochastic Processes.
700	1		_aZeitouni, Ofer. _eauthor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9783642033100
830		0	_aStochastic Modelling and Applied Probability, _x0172-4568 ; _v38
856	4	0	_uhttp://dx.doi.org/10.1007/978-3-642-03311-7
912			_aZDB-2-SMA
999			_c111489 _d111489