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Applied Probability Models with Optimization Applications (Dover Books on Mathematics)by Sheldon M. Ross
Synopses & ReviewsPublisher Comments:Concise advancedlevel introduction to stochastic processes that frequently arise in applied probability. Largely selfcontained text covers Poisson process, renewal theory, Markov chains, inventory theory, Brownian motion and continuous time optimization models, much more. Problems and references at chapter ends. "Excellent introduction." — Journal of the American Statistical Association. Bibliography. 1970 edition. Synopsis:Concise advancedlevel introduction to stochastic processes that arise in applied probability. Poisson process, renewal theory, Markov chains, Brownian motion, much more. Problems. References. Bibliography. 1970 edition. Table of Contents1. INTRODUCTION TO STOCHASTIC PROCESSES
1.1. Random Variables and Probability Theory 1.2. Conditional Expectation 1.3. Stochatic Processes Problems 2. THE POISSON RPCESS 2.1 Introduction and Definitions 2.2 Interarrival and Waiting Time Distributions 2.3 Conditional Distribution of the Arrival Times 2.4 Compound and Nonhomogenous Poisson Processes 2.5 Stationary Point Processes Problems References 3. RENEWAL THEORY 3.1 Introduction and Preliminaries 3.2 Renewal Equation and Generalizations 3.3 Limit Theorems 3.4 Wald's Equation 3.5 Back to Renewal Theory 3.6 Excess Life and Age Distribution 3.7 Delayed Renewal Processes 3.8 Counter Models 3.9 Renewal Reward Process 3.10 Nonterminating versus Terminating Renewal Processes 3.11 Age Dependent Branching Processes Problems References 4. MARKOV CHAINS 4.1 Preliminaries and Examples 4.2 Classification of States 4.3 Limit Theorems 4.4 Transitions Among Classes 4.5 Branching Processes 4.6 Transient States Problems References 5. "SEMIMARKOV, MARKOV RENEWAL AND REGERNERATIVE PROCESSES" 5.1 Introduction and Preliminaries 5.2 Classification of States 5.3 Some Simple Relationships 5.4 Regenerative Processes 5.5 A Queueing Application 5.6 Back to Markov Renewal ProcessesLimiting Probabilities 5.7 Limiting Distributions of the Markov Renewal Process 5.8 Continuous Time Markov Chains 5.9 Birth and Death Processes Problems References 6. MARKOV DECISION PROCESSES 6.1 Introduction 6.2 Expected Discounted Cost 6.3 Some Examples 6.4 "Positive Costs, No Discounting" 6.5 Applications: Optimal Stopping and Sequential Analysis 6.6 Expected Average Cost CriterionIntroduction and Counter examples 6.7 Expected Average Cost Criterion 6.8 Finite State SpaceComputational Approaches Problems References 7. SEMIMARKOV DECISION PROCESSES 7.1 Introduction 7.2 Discounted Cost Criterion 7.3 Average CostPreliminaries and Equality of Criteria 7.4 Average CostResults 7.5 Some Examples Problems References 8. INVENTORY THEORY 8.1 Introduction 8.2 A Single Period Model 8.3 MultiPeriod Models 8.4 A MultiPeriod Stationary Optimal Policy 8.5 Inventory Issuing Policies Problems References 9. BROWNIAN MOTION AND CONTINUOUS TIME OPTIMIZATION MODELS 9.1 Introduction and Preliminaries 9.2 Maximum of the Wiener Process 9.3 The Wiener Process and Optimization 9.4 The Maximum VariableA Renewal Application 9.5 Optimal Dispatching of a Poisson Process 9.6 Infinitesimal LookAhead Stopping Rules Problems Reference APPENDICES INDEX What Our Readers Are SayingBe the first to add a comment for a chance to win!Product Details
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