04480nam 22005655 450 991097026560332120250811094923.01-4612-2726-710.1007/978-1-4612-2726-7(CKB)3400000000090081(SSID)ssj0001297252(PQKBManifestationID)11725924(PQKBTitleCode)TC0001297252(PQKBWorkID)11361998(PQKB)10323352(DE-He213)978-1-4612-2726-7(MiAaPQ)EBC3076088(PPN)23804064X(EXLCZ)99340000000009008120121227d1993 u| 0engurnn|008mamaatxtccrAn Introduction to Probability and Stochastic Processes /by Marc A. Berger1st ed. 1993.New York, NY :Springer New York :Imprint: Springer,1993.1 online resource (XII, 205 p.) Springer Texts in Statistics,2197-4136Bibliographic Level Mode of Issuance: Monograph0-387-97784-8 1-4612-7643-8 Includes bibliographical references and index.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).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 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.Springer Texts in Statistics,2197-4136ProbabilitiesProbability TheoryProbabilities.Probability Theory.519.2Berger Marc Aauthttp://id.loc.gov/vocabulary/relators/aut251785MiAaPQMiAaPQMiAaPQBOOK9910970265603321Introduction to probability and stochastic processes635667UNINA