{"product_id":"large-deviations-for-markov-chains-hardback-9781316511893","title":"Large Deviations for Markov Chains (Hardback) 9781316511893","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eLarge Deviations for Markov Chains\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eA study of large deviations for empirical measures and vector-valued additive functionals of general state space Markov chains.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eAlejandro D. de Acosta (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781316511893, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 27 October 2022\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e230 pages\u003cbr\u003e23.5 x 15.8 x 2.2 cm, 0.55 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cem\u003e\u003cfont size=\"3\"\u003e'The theory of large deviations is an important way to understand many mathematical and physical models. This book covers the fascinating topic of large deviations for empirical measures and additive functionals of Markov chains with general state space, a subject on which the author is a leading expert who has made crucial contributions. Markov chains represent a large class of stochastic models with a wide spectrum of behaviors. It is remarkable that any universal results, like the ones given in the book, can be formulated for such a large family. It is equally remarkable that the book develops a sharp link between the large deviations and the degree of recurrence of Markov chains. The book does a superb job of clarification, comparison and identification of the rate functions that govern the large deviations.' Xia Chen, University of Tennessee\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eThis book studies the large deviations for empirical measures and vector-valued additive functionals of Markov chains with general state space. Under suitable recurrence conditions, the ergodic theorem for additive functionals of a Markov chain asserts the almost sure convergence of the averages of a real or vector-valued function of the chain to the mean of the function with respect to the invariant distribution. In the case of empirical measures, the ergodic theorem states the almost sure convergence in a suitable sense to the invariant distribution. The large deviation theorems provide precise asymptotic estimates at logarithmic level of the probabilities of deviating from the preponderant behavior asserted by the ergodic theorems.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePreface\u003cbr\u003e 1. Introduction\u003cbr\u003e 2. Lower bounds and a property of lambda\u003cbr\u003e 3. Upper bounds I\u003cbr\u003e 4. Identification and reconciliation of rate functions\u003cbr\u003e 5. Necessary conditions – bounds on the rate function, invariant measures, irreducibility and recurrence\u003cbr\u003e 6. Upper bounds II – equivalent analytic conditions\u003cbr\u003e 7. Upper bounds III – sufficient conditions\u003cbr\u003e 8. The large deviations principle for empirical measures\u003cbr\u003e 9. The case when S is countable and P is matrix irreducible\u003cbr\u003e 10. Examples\u003cbr\u003e 11. Large deviations for vector-valued additive functionals\u003cbr\u003e Appendix A\u003cbr\u003e Appendix B\u003cbr\u003e Appendix C\u003cbr\u003e Appendix D\u003cbr\u003e Appendix E\u003cbr\u003e Appendix F\u003cbr\u003e Appendix G\u003cbr\u003e Appendix H\u003cbr\u003e Appendix I\u003cbr\u003e Appendix J\u003cbr\u003e Appendix K\u003cbr\u003e References\u003cbr\u003e Author index\u003cbr\u003e Subject index.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Stochastics [\u003ca title=\"See our other books on Stochastics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Stochastics%20%5BPBWL%5D%22\"\u003ePBWL\u003c\/a\u003e], Topology [\u003ca title=\"See our other books on Topology\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Topology%20%5BPBP%5D%22\"\u003ePBP\u003c\/a\u003e], Functional analysis \u0026amp; transforms [\u003ca title=\"See our other books on Functional analysis \u0026amp; transforms\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Functional%20analysis%20\u0026amp;%20transforms%20%5BPBKF%5D%22\"\u003ePBKF\u003c\/a\u003e], Real analysis, real variables [\u003ca title=\"See our other books on Real analysis, real variables\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Real%20analysis,%20real%20variables%20%5BPBKB%5D%22\"\u003ePBKB\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":46266463846680,"sku":"9781316511893","price":82.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9781316511893i_b9e87688-4ba1-4ceb-b427-2211f56dd412.jpg?v=1696681588","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/large-deviations-for-markov-chains-hardback-9781316511893","provider":"Freshly Printed Books","version":"1.0","type":"link"}