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[null,"1.","Record Nr.",null,"UNINA9910970265603321"]
[null,null,"Autore",null,"Berger Marc A"]
[null,null,"Titolo",null,"An Introduction to Probability and Stochastic Processes / / by Marc A. Berger"]
[null,null,"Pubbl/distr/stampa",null,"New York, NY : , : Springer New York : , : Imprint : Springer, , 1993"]
[null,null,"ISBN",null,"1-4612-2726-7"]
[null,null,"Edizione",null,"[1st ed. 1993.]"]
[null,null,"Descrizione fisica",null,"1 online resource (XII, 205 p.)"]
[null,null,"Collana",null,"Springer Texts in Statistics, , 2197-4136"]
[null,null,"Disciplina",null,"519.2"]
[null,null,"Soggetti",null,"Probabilities"]
[{"$nulls":4},"Probability Theory"]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Monografia"]
[null,null,null,"Note generali","Bibliographic Level Mode of Issuance: Monograph"]
[null,null,null,"Nota di bibliografia","Includes bibliographical references and index."]
[null,null,"Nota di contenuto",null,"I. Univariate Random Variables -- Discrete Random Variables -- Properties of Expectation -- Properties of Characteristic Functions -- Basic Distributions -- Absolutely Continuous Random Variables -- Basic Distributions -- Distribution Functions -- Computer Generation of Random Variables -- Exercises -- II. Multivariate Random Variables -- Joint Random Variables -- Conditional Expectation -- Orthogonal Projections -- Joint Normal Distribution -- Multi-Dimensional Distribution Functions -- Exercises -- III. Limit Laws -- Law of Large Numbers -- Weak Convergence -- Bochner’s Theorem -- Extremes -- Extremal Distributions -- Large Deviations -- Exercises -- IV. Markov Chains—Passage Phenomena -- First Notions and Results -- Limiting Diffusions -- Branching Chains -- Queueing Chains -- Exercises -- V. Markov Chains—Stationary Distributions and Steady State -- Stationary Distributions -- Geometric Ergodicity -- Examples -- Exercises -- VI. Markov Jump Processes -- Pure Jump Processes -- Poisson Process -- Birth and Death Process -- Exercises -- VII. Ergodic Theory with an Application to Fractals -- Ergodic Theorems -- Subadditive Ergodic Theorem -- Products of Random Matrices -- Oseledec’s Theorem -- Fractals -- Bibliographical Comments -- Exercises -- References -- Solutions (Sections I–V)."]
[null,null,null,"Sommario/riassunto","These notes were written as a result of my having taught a \"nonmeasure theoretic\" course in probability and stochastic processes a few times at the Weizmann Institute in Israel. I have tried to follow two principles. The first is to prove things \"probabilistically\" whenever possible without recourse to other branches of mathematics and in a notation that is as \"probabilistic\" as possible. Thus, for example, the "]
[{"$nulls":4},"asymptotics of pn for large n, where P is a stochastic matrix, is developed in Section V by using passage probabilities and hitting times rather than, say, pulling in Perron­ Frobenius theory or spectral analysis. Similarly in Section II the joint normal distribution is studied through conditional expectation rather than quadratic forms. The second principle I have tried to follow is to only prove results in their simple forms and to try to eliminate any minor technical com­ putations from proofs, so as to expose the most important steps. Steps in proofs or derivations that involve algebra or basic calculus are not shown; only steps involving, say, the use of independence or a dominated convergence argument or an assumptjon in a theorem are displayed. For example, in proving inversion formulas for characteristic functions I omit steps involving evaluation of basic trigonometric integrals and display details only where use is made of Fubini's Theorem or the Dominated Convergence Theorem."]