An Introduction to Stochastic Processes
Duxbury Press (Verlag)
978-0-534-25518-3 (ISBN)
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Instead of the standard formal and mathematically rigorous approach usual for texts for this course, Edward Kao emphasizes the development of operational skills and analysis through a variety of well-chosen examples.
1. INTRODUCTION
Overview / Introduction / Discrete Random Variables and Generating Functions / Continuous Random Variables and Laplace Transforms / Some Mathematical Background / Problems / Bibliographic Notes / References / Appendix
2. POISSON PROCESSES
Overview / Introduction / Properties of Poisson Processes / Nonhomogeneous Poisson Processes / Filtered Poisson Processes / Two-Dimensional and Marked Poisson Processes / Poisson Arrivals See Time Averages (PASTA) / Problems / Bibliographic Notes / References / Appendix
3. RENEWAL PROCESSES
Overview / Introduction / Renewal-Type Equations / Excess Life, Current Life, and Total Life / Renewal Reward Processes / Limiting Theorems, Stationary and Transient Renewal Processes / Regenerative Processes / Discrete Renewal Processes / Problems / Bibliographic Notes / References / Appendix
4. DISCRETE-TIME MARKOV CHAINS
Overview / Introduction / Classification of States / Ergodic and Periodic Markov Chains / Absorbing Markov Chains / Markov Reward Processes / Reversible Discrete-Time Markov Chains / Problems / Bibliographic Notes / References / Appendix
5. CONTINUOUS-TIME MARKOV CHAINS
Overview / Introduction / The Kolmogorov Differential Equations / The Limiting Probabilities / Absorbing Continuous-Time Markov Chains / Phase-Type Distributions / Uniformization / Continuous-Time Markov Reward Processes / Reversible Continuous-Time Markov Chains / Problems / Bibliographic Notes / References / Appendix
6. MARKOV RENEWAL AND SEMI-REGENERATIVE PROCESSES
Overview / Introduction / Markov Renewal Functions and Equations / Semi-Markov Processes and Related Reward Processes / Semi-Regenerative Processes / Problems / Bibliographic Notes / References / Appendix
7. BROWNIAN MOTION AND OTHER DIFFUSION PROCESSES
Overview / Introduction / Diffusion Processes / Ito''''s Calculus and Stochastic Differential Equations / Multidimensional Ito''''s Lemma / Control of Systems of Stochastic Differential Equations / Problems / Bibliographic Notes / References / Appendix / APPENDIX: GETTING STARTED WITH MATLAB / INDEX
| Sprache | englisch |
|---|---|
| Maße | 168 x 243 mm |
| Gewicht | 762 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik |
| ISBN-10 | 0-534-25518-3 / 0534255183 |
| ISBN-13 | 978-0-534-25518-3 / 9780534255183 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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