LEADER 04860nam 22006135 450 001 9910789349903321 005 20211118203801.0 010 $a1-4471-0533-8 024 7 $a10.1007/978-1-4471-0533-6 035 $a(CKB)3400000000088190 035 $a(SSID)ssj0000805273 035 $a(PQKBManifestationID)11517481 035 $a(PQKBTitleCode)TC0000805273 035 $a(PQKBWorkID)10836282 035 $a(PQKB)11281651 035 $a(DE-He213)978-1-4471-0533-6 035 $a(MiAaPQ)EBC3073471 035 $a(PPN)237990296 035 $a(EXLCZ)993400000000088190 100 $a20121227d1999 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aBasic Stochastic Processes$b[electronic resource] $eA Course Through Exercises /$fby Zdzislaw Brzezniak, Tomasz Zastawniak 205 $a1st ed. 1999. 210 1$aLondon :$cSpringer London :$cImprint: Springer,$d1999. 215 $a1 online resource (X, 226 p.) 225 1 $aSpringer Undergraduate Mathematics Series,$x1615-2085 300 $aIncludes index. 300 $a"With 21 Figures." 311 $a3-540-76175-6 327 $a1. Review of Probability -- 1.1 Events and Probability -- 1.2 Random Variables -- 1.3 Conditional Probability and Independence -- 1.4 Solutions -- 2. Conditional Expectation -- 2.1 Conditioning on an Event -- 2.2 Conditioning on a Discrete Random Variable -- 2.3 Conditioning on an Arbitrary Random Variable -- 2.4 Conditioning on a ?-Field -- 2.5 General Properties -- 2.6 Various Exercises on Conditional Expectation -- 2.7 Solutions -- 3. Martingales in Discrete -- 3.1 Sequences of Random Variables -- 3.2 Filtrations -- 3.3 Martingales -- 3.4 Games of Chance -- 3.5 Stopping Times -- 3.6 Optional Stopping Theorem -- 3.7 Solutions -- 4. Martingale Inequalities and Convergence -- 4.1 Doob?s Martingale Inequalities -- 4.2 Doob?s Martingale Convergence Theorem -- 4.3 Uniform Integrability and L1 Convergence of Martingales -- 4.4 Solutions -- 5. Markov Chains -- 5.1 First Examples and Definitions -- 5.2 Classification of States -- 5.3 Long-Time Behaviour of Markov Chains: General Case -- 5.4 Long-Time Behaviour of Markov Chains with Finite State Space -- 5.5 Solutions -- 6. Stochastic Processes in Continuous Time -- 6.1 General Notions -- 6.2 Poisson Process -- 6.3 Brownian Motion -- 6.4 Solutions -- 7. Itô Stochastic Calculus -- 7.1 Itô Stochastic Integral: Definition -- 7.2 Examples -- 7.3 Properties of the Stochastic Integral -- 7.4 Stochastic Differential and Itô Formula -- 7.5 Stochastic Differential Equations -- 7.6 Solutions. 330 $aThis book has been designed for a final year undergraduate course in stochastic processes. It will also be suitable for mathematics undergraduates and others with interest in probability and stochastic processes, who wish to study on their own. The main prerequisite is probability theory: probability measures, random variables, expectation, independence, conditional probability, and the laws of large numbers. The only other prerequisite is calculus. This covers limits, series, the notion of continuity, differentiation and the Riemann integral. Familiarity with the Lebesgue integral would be a bonus. A certain level of fundamental mathematical experience, such as elementary set theory, is assumed implicitly. Throughout the book the exposition is interlaced with numerous exercises, which form an integral part of the course. Complete solutions are provided at the end of each chapter. Also, each exercise is accompanied by a hint to guide the reader in an informal manner. This feature will be particularly useful for self-study and may be of help in tutorials. It also presents a challenge for the lecturer to involve the students as active participants in the course. 410 0$aSpringer Undergraduate Mathematics Series,$x1615-2085 606 $aProbabilities 606 $aObservations, Astronomical 606 $aAstronomy?Observations 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 606 $aAstronomy, Observations and Techniques$3https://scigraph.springernature.com/ontologies/product-market-codes/P22014 615 0$aProbabilities. 615 0$aObservations, Astronomical. 615 0$aAstronomy?Observations. 615 14$aProbability Theory and Stochastic Processes. 615 24$aAstronomy, Observations and Techniques. 676 $a519.2 686 $a60Gxx$2msc 700 $aBrzezniak$b Zdzislaw$4aut$4http://id.loc.gov/vocabulary/relators/aut$0352211 702 $aZastawniak$b Tomasz$4aut$4http://id.loc.gov/vocabulary/relators/aut 906 $aBOOK 912 $a9910789349903321 996 $aBasic Stochastic Processes$93727094 997 $aUNINA