LEADER 05027oam 2200517 450 001 9910792485203321 005 20190911100030.0 010 $a0-12-407839-7 035 $a(OCoLC)848902271 035 $a(MiFhGG)GVRL8DZX 035 $a(EXLCZ)992660000000011104 100 $a20130315d2013 uy 0 101 0 $aeng 135 $aurun|---uuuua 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aMarkov processes for stochastic modeling /$fOliver C. Ibe, University of Massachusetts, Lowell, MA, USA 205 $a2nd ed. 210 $aAmsterdam, Netherlands $cElsevier$dc2013 210 1$aLondon :$cElsevier,$d2013. 215 $a1 online resource (xviii, 494 pages) $cillustrations 225 0 $aElsevier insights Markov processes for stochastic modeling 300 $aPrevious edition: Amsterdam; London: Academic, 2009. 311 $a0-12-407795-1 320 $aIncludes bibliographical references. 327 $aFront Cover; Markov Processes for Stochastic Modeling; Copyright page; Contents; Acknowledgments; Preface to the Second Edition; Preface to the First Edition; 1 Basic Concepts in Probability; 1.1 Introduction; 1.1.1 Conditional Probability; 1.1.2 Independence; 1.1.3 Total Probability and the Bayes' Theorem; 1.2 Random Variables; 1.2.1 Distribution Functions; 1.2.2 Discrete Random Variables; 1.2.3 Continuous Random Variables; 1.2.4 Expectations; 1.2.5 Expectation of Nonnegative Random Variables; 1.2.6 Moments of Random Variables and the Variance; 1.3 Transform Methods; 1.3.1 The s-Transform 327 $a1.3.2 The z-Transform1.4 Bivariate Random Variables; 1.4.1 Discrete Bivariate Random Variables; 1.4.2 Continuous Bivariate Random Variables; 1.4.3 Covariance and Correlation Coefficient; 1.5 Many Random Variables; 1.6 Fubini's Theorem; 1.7 Sums of Independent Random Variables; 1.8 Some Probability Distributions; 1.8.1 The Bernoulli Distribution; 1.8.2 The Binomial Distribution; 1.8.3 The Geometric Distribution; 1.8.4 The Pascal Distribution; 1.8.5 The Poisson Distribution; 1.8.6 The Exponential Distribution; 1.8.7 The Erlang Distribution; 1.8.8 Normal Distribution; 1.9 Limit Theorems 327 $a1.9.1 Markov Inequality1.9.2 Chebyshev Inequality; 1.9.3 Laws of Large Numbers; 1.9.4 The Central Limit Theorem; 1.10 Problems; 2 Basic Concepts in Stochastic Processes; 2.1 Introduction; 2.2 Classification of Stochastic Processes; 2.3 Characterizing a Stochastic Process; 2.4 Mean and Autocorrelation Function of a Stochastic Process; 2.5 Stationary Stochastic Processes; 2.5.1 Strict-Sense Stationary Processes; 2.5.2 Wide-Sense Stationary Processes; 2.6 Ergodic Stochastic Processes; 2.7 Some Models of Stochastic Processes; 2.7.1 Martingales; Stopping Times; 2.7.2 Counting Processes 327 $a2.7.3 Independent Increment Processes2.7.4 Stationary Increment Process; 2.7.5 Poisson Processes; Interarrival Times for the Poisson Process; Compound Poisson Process; Combinations of Independent Poisson Processes; Competing Independent Poisson Processes; Subdivision of a Poisson Process; 2.8 Problems; 3 Introduction to Markov Processes; 3.1 Introduction; 3.2 Structure of Markov Processes; 3.3 Strong Markov Property; 3.4 Applications of Discrete-Time Markov Processes; 3.4.1 Branching Processes; 3.4.2 Social Mobility; 3.4.3 Markov Decision Processes 327 $a3.5 Applications of Continuous-Time Markov Processes3.5.1 Queueing Systems; 3.5.2 Continuous-Time Markov Decision Processes; 3.5.3 Stochastic Storage Systems; 3.6 Applications of Continuous-State Markov Processes; 3.6.1 Application of Diffusion Processes to Financial Options; 3.6.2 Applications of Brownian Motion; 3.7 Summary; 4 Discrete-Time Markov Chains; 4.1 Introduction; 4.2 State-Transition Probability Matrix; 4.2.1 The n-Step State-Transition Probability; 4.3 State-Transition Diagrams; 4.4 Classification of States; 4.5 Limiting-State Probabilities; 4.5.1 Doubly Stochastic Matrix 327 $a4.6 Sojourn Time 330 $aMarkov processes are processes that have limited memory. In particular, their dependence on the past is only through the previous state. They are used to model the behavior of many systems including communications systems, transportation networks, image segmentation and analysis, biological systems and DNA sequence analysis, random atomic motion and diffusion in physics, social mobility, population studies, epidemiology, animal and insect migration, queueing systems, resource management, dams, financial engineering, actuarial science, and decision systems. Covering a wide range of 410 0$aElsevier insights. 606 $aMarkov processes 606 $aStochastic processes 615 0$aMarkov processes. 615 0$aStochastic processes. 676 $a519.233 700 $aIbe$b Oliver C$0522175 801 0$bMiFhGG 801 1$bMiFhGG 906 $aBOOK 912 $a9910792485203321 996 $aMarkov processes for stochastic modeling$93732486 997 $aUNINA