LEADER 05615nam 22006975 450 001 9910832977703321 005 20250725073253.0 010 $a9781461523291 010 $a146152329X 024 7 $a10.1007/978-1-4615-2329-1 035 $a(CKB)3400000000094829 035 $a(SSID)ssj0001007804 035 $a(PQKBManifestationID)11556825 035 $a(PQKBTitleCode)TC0001007804 035 $a(PQKBWorkID)10955055 035 $a(PQKB)10733264 035 $a(DE-He213)978-1-4615-2329-1 035 $a(MiAaPQ)EBC3080044 035 $a(MiAaPQ)EBC6871846 035 $a(Au-PeEL)EBL6871846 035 $a(PPN)237921723 035 $a(ScCtBLL)cff9bcad-63e2-44b7-a40b-904be9f87cfb 035 $a(OCoLC)1000336239 035 $a(EXLCZ)993400000000094829 100 $a20121227d1996 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aDiscrete Stochastic Processes /$fby Robert G. Gallager 205 $a1st ed. 1996. 210 1$aNew York, NY :$cSpringer US :$cImprint: Springer,$d1996. 215 $a1 online resource (XIII, 271 p.) 225 1 $aThe Springer International Series in Engineering and Computer Science ;$v321 300 $aBibliographic Level Mode of Issuance: Monograph 311 08$a9780792395836 311 08$a0792395832 311 08$a9781461359869 311 08$a1461359864 320 $aIncludes bibliographical references (pages [265]-265) and index. 327 $a1 Introduction and Probability Review -- 1.1 Introduction -- 1.2 Probability Review -- 1.3 Conditional Probabilities -- 1.4 Random Variables -- 1.5 Expectations -- 1.6 Transforms -- 1.7 Weak Law of Large Numbers -- 1.8 Strong Law of Large Numbers -- 1.9 Summary -- Table of Standard Random Variables -- Exercises -- Notes -- 2 Poisson Processes -- 2.1 Introduction -- 2.2 Definition and Properties of the Poisson Process -- 2.3 Combinations and Subdivisions of Independent Poisson Processes -- 2.4 Non-Homogeneous Poisson Processes -- 2.5 Order Statistics and Conditional Arrival Epochs -- 2.6 Summary -- Exercises -- Notes -- 3 Renewal Processes -- 3.1 Introduction -- 3.2 Strong Law of Large Numbers for Renewal Processes -- 3.3 Expected Number of Renewals -- 3.4 Renewal Reward Processes; Time Averages -- 3.5 Renewal Reward Processes; Ensemble Averages -- 3.6 Applications of Renewal Reward Theory -- 3.7 Delayed Renewal Processes -- 3.8 Summary -- Exercises -- Notes -- 4 Finite State Markov Chains -- 4.1 Introduction -- 4.2 Classification of States -- 4.3 The Matrix Representation -- 4.4 Perron?Frobenius Theory -- 4.5 Markov Chains with Rewards -- 4.6 Markov Decision Theory and Dynamic Programming -- 4.7 Summary -- Exercises -- Notes -- 5 Markov Chains with Countably Infinite State Spaces -- 5.1 Introduction and Classification of States -- 5.2 Branching Processes -- 5.3 Birth Death Markov Chains -- 5.4 Reversible Markov Chains -- 5.5 The M/M/1 Sampled Time Markov Chain -- 5.6 Round-Robin and Processor Sharing -- 5.7 Semi-Markov Processes -- 5.8 Example?M/G/1 Queue -- 5.9 Summary -- Exercises -- 6 Markov Processes with Countable State Spaces -- 6.1 Introduction -- 6.2 The Kolmogorov Differential Equations -- 6.3 Uniformization -- 6.4 Birth Death Processes -- 6.5 Reversibility for Markov Processes -- 6.6 Jackson Networks -- ClosedJackson Networks -- 6.7 Summary -- Exercises -- 7 Random Walks and Martingales -- 7.1 Introduction -- 7.2 The G/G/1 Queue -- 7.3 Detection, Decisions, and Hypothesis Testing -- 7.4 Threshold Crossing Probabilities -- 7.5 Wald?s Identity and Walks with Two Thresholds -- 7.6 Martingales and Submartingales -- 7.7 Stopped Processes and Stopping Rules -- 7.8 The Kolmogorov Inequalities -- 7.9 Summary -- Exercises -- Notes. 330 $aStochastic processes are found in probabilistic systems that evolve with time. Discrete stochastic processes change by only integer time steps (for some time scale), or are characterized by discrete occurrences at arbitrary times. Discrete Stochastic Processes helps the reader develop the understanding and intuition necessary to apply stochastic process theory in engineering, science and operations research. The book approaches the subject via many simple examples which build insight into the structure of stochastic processes and the general effect of these phenomena in real systems. The book presents mathematical ideas without recourse to measure theory, using only minimal mathematical analysis. In the proofs and explanations, clarity is favored over formal rigor, and simplicity over generality. Numerous examples are given to show how results fail to hold when all the conditions are not satisfied. Audience: An excellent textbook for a graduate level course in engineering and operations research. Also an invaluable reference for all those requiring a deeper understanding of the subject. 410 0$aThe Springer International Series in Engineering and Computer Science ;$v321 606 $aElectrical engineering 606 $aOperations research 606 $aElectrical and Electronic Engineering 606 $aOperations Research and Decision Theory 615 0$aElectrical engineering. 615 0$aOperations research. 615 14$aElectrical and Electronic Engineering. 615 24$aOperations Research and Decision Theory. 676 $a519.2 700 $aGallager$b Robert G.$08401 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910832977703321 996 $aDiscrete stochastic processes$9328665 997 $aUNINA