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008 121227s2001 gw | s |||| 0|eng d
020 _a9783540446231
_9978-3-540-44623-1
024 7 _a10.1007/b87874
_2doi
050 4 _aQA273.A1-274.9
050 4 _aQA274-274.9
072 7 _aPBT
_2bicssc
072 7 _aMAT029000
_2bisacsh
072 7 _aPBT
_2thema
072 7 _aPBWL
_2thema
082 0 4 _a519.2
_223
245 1 0 _aLimit Theorems for Markov Chains and Stochastic Properties of Dynamical Systems by Quasi-Compactness
_h[electronic resource] /
_cedited by Hubert Hennion, Loïc Hervé.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2001.
300 _aVIII, 152 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1766
505 0 _aGeneral Facts About The Method Purpose Of The Paper -- The Central Limit Theorems For Markov Chains Theorems A, B, C -- Quasi-Compact Operators of Diagonal Type And Their Perturbations -- First Properties of Fourier Kernels Application -- Peripheral Eigenvalues of Fourier Kernels -- Proofs Of Theorems A, B, C -- Renewal Theorem For Markov Chains Theorem D -- Large Deviations For Markov Chains Theorem E -- Ergodic Properties For Markov Chains -- Markov Chains Associated With Lipschitz Kernels Examples -- Stochastic Properties Of Dynamical Systems Theorems A*, B*, C*, D*, E* -- Expanding Maps -- Proofs Of Some Statements In Probability Theory -- Functional Analysis Results On Quasi-Compactness -- Generalization To The Non-Ergodic Case.
520 _aThe usefulness of from the of techniques perturbation theory operators, to kernel for limit theorems for a applied quasi-compact positive Q, obtaining Markov chains for stochastic of or dynamical by describing properties systems, of Perron- Frobenius has been demonstrated in several All use a operator, papers. these works share the features the features that must be same specific general ; used in each stem from the nature of the functional particular case precise space where the of is and from the number of quasi-compactness Q proved eigenvalues of of modulus 1. We here a functional framework for Q give general analytical this method and we the aforementioned behaviour within it. It asymptotic prove is worth that this framework is to allow the unified noticing sufficiently general treatment of all the cases considered in the literature the previously specific ; characters of model translate into the verification of of simple hypotheses every a functional nature. When to Markov kernels or to Perr- applied Lipschitz Frobenius associated with these statements rise operators expanding give maps, to new results and the of known The main clarify proofs already properties. of the deals with a Markov kernel for which 1 is a part quasi-compact Q paper of modulus 1. An essential but is not the simple eigenvalue unique eigenvalue element of the work is the of the of peripheral Q precise description spectrums and of its To conclude the the results obtained perturbations.
650 0 _aDistribution (Probability theory.
650 0 _aGlobal analysis (Mathematics).
650 0 _aDifferential Equations.
650 1 4 _aProbability Theory and Stochastic Processes.
_0http://scigraph.springernature.com/things/product-market-codes/M27004
650 2 4 _aAnalysis.
_0http://scigraph.springernature.com/things/product-market-codes/M12007
650 2 4 _aOrdinary Differential Equations.
_0http://scigraph.springernature.com/things/product-market-codes/M12147
700 1 _aHennion, Hubert.
_eeditor.
_4edt
_4http://id.loc.gov/vocabulary/relators/edt
700 1 _aHervé, Loïc.
_eeditor.
_4edt
_4http://id.loc.gov/vocabulary/relators/edt
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783662205389
776 0 8 _iPrinted edition:
_z9783540424154
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1766
856 4 0 _uhttps://doi.org/10.1007/b87874
912 _aZDB-2-SMA
912 _aZDB-2-LNM
912 _aZDB-2-BAE
999 _c12055
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