LEADER 04480nam 22005655 450 001 9910970265603321 005 20250811094923.0 010 $a1-4612-2726-7 024 7 $a10.1007/978-1-4612-2726-7 035 $a(CKB)3400000000090081 035 $a(SSID)ssj0001297252 035 $a(PQKBManifestationID)11725924 035 $a(PQKBTitleCode)TC0001297252 035 $a(PQKBWorkID)11361998 035 $a(PQKB)10323352 035 $a(DE-He213)978-1-4612-2726-7 035 $a(MiAaPQ)EBC3076088 035 $a(PPN)23804064X 035 $a(EXLCZ)993400000000090081 100 $a20121227d1993 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 13$aAn Introduction to Probability and Stochastic Processes /$fby Marc A. Berger 205 $a1st ed. 1993. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Springer,$d1993. 215 $a1 online resource (XII, 205 p.) 225 1 $aSpringer Texts in Statistics,$x2197-4136 300 $aBibliographic Level Mode of Issuance: Monograph 311 08$a0-387-97784-8 311 08$a1-4612-7643-8 320 $aIncludes bibliographical references and index. 327 $aI. 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). 330 $aThese notes were written as a result of my having taught a "nonmeasure theoretic" course in probability and stochastic processes a few times at the Weizmann Institute in Israel. I have tried to follow two principles. The first is to prove things "probabilistically" whenever possible without recourse to other branches of mathematics and in a notation that is as "probabilistic" as possible. Thus, for example, the asymptotics of pn for large n, where P is a stochastic matrix, is developed in Section V by using passage probabilities and hitting times rather than, say, pulling in Perron­ Frobenius theory or spectral analysis. Similarly in Section II the joint normal distribution is studied through conditional expectation rather than quadratic forms. The second principle I have tried to follow is to only prove results in their simple forms and to try to eliminate any minor technical com­ putations from proofs, so as to expose the most important steps. Steps in proofs or derivations that involve algebra or basic calculus are not shown; only steps involving, say, the use of independence or a dominated convergence argument or an assumptjon in a theorem are displayed. For example, in proving inversion formulas for characteristic functions I omit steps involving evaluation of basic trigonometric integrals and display details only where use is made of Fubini's Theorem or the Dominated Convergence Theorem. 410 0$aSpringer Texts in Statistics,$x2197-4136 606 $aProbabilities 606 $aProbability Theory 615 0$aProbabilities. 615 14$aProbability Theory. 676 $a519.2 700 $aBerger$b Marc A$4aut$4http://id.loc.gov/vocabulary/relators/aut$0251785 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910970265603321 996 $aIntroduction to probability and stochastic processes$9635667 997 $aUNINA