Continuous-Time Markov Chains and Applications: A Singular Perturbation Approach
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1998
|
| Schriftenreihe: | Applications of Mathematics, Stochastic Modelling and Applied Probability
37 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This book is concerned with continuous-time Markov chains. It develops an integrated approach to singularly perturbed Markovian systems, and reveals interrelations of stochastic processes and singular perturbations. In recent years, Markovian formulations have been used routinely for nu merous real-world systems under uncertainties. Quite often, the underlying Markov chain is subject to rather frequent fluctuations and the correspond ing states are naturally divisible to a number of groups such that the chain fluctuates very rapidly among different states within a group, but jumps less frequently from one group to another. Various applications in engineer ing, economics, and biological and physical sciences have posed increasing demands on an in-depth study of such systems. A basic issue common to many different fields is the understanding of the distribution and the struc ture of the underlying uncertainty. Such needs become even more pressing when we deal with complex and/or large-scale Markovian models, whose closed-form solutions are usually very difficult to obtain. Markov chain, a well-known subject, has been studied by a host of re searchers for many years. While nonstationary cases have been treated in the literature, much emphasis has been on stationary Markov chains and their basic properties such as ergodicity, recurrence, and stability. In contrast, this book focuses on singularly perturbed nonstationary Markov chains and their asymptotic properties. Singular perturbation theory has a long history and is a powerful tool for a wide variety of applications |
| Beschreibung: | 1 Online-Ressource (XV, 351 p) |
| ISBN: | 9781461206279 9781461268444 |
| ISSN: | 0172-4568 |
| DOI: | 10.1007/978-1-4612-0627-9 |
Internformat
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| 500 | |a This book is concerned with continuous-time Markov chains. It develops an integrated approach to singularly perturbed Markovian systems, and reveals interrelations of stochastic processes and singular perturbations. In recent years, Markovian formulations have been used routinely for nu merous real-world systems under uncertainties. Quite often, the underlying Markov chain is subject to rather frequent fluctuations and the correspond ing states are naturally divisible to a number of groups such that the chain fluctuates very rapidly among different states within a group, but jumps less frequently from one group to another. Various applications in engineer ing, economics, and biological and physical sciences have posed increasing demands on an in-depth study of such systems. A basic issue common to many different fields is the understanding of the distribution and the struc ture of the underlying uncertainty. Such needs become even more pressing when we deal with complex and/or large-scale Markovian models, whose closed-form solutions are usually very difficult to obtain. Markov chain, a well-known subject, has been studied by a host of re searchers for many years. While nonstationary cases have been treated in the literature, much emphasis has been on stationary Markov chains and their basic properties such as ergodicity, recurrence, and stability. In contrast, this book focuses on singularly perturbed nonstationary Markov chains and their asymptotic properties. Singular perturbation theory has a long history and is a powerful tool for a wide variety of applications | ||
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Datensatz im Suchindex
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4612-0627-9 |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:05Z |
| institution | BVB |
| isbn | 9781461206279 9781461268444 |
| issn | 0172-4568 |
| language | English |
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| series2 | Applications of Mathematics, Stochastic Modelling and Applied Probability |
| spelling | Yin, G. George Verfasser aut Continuous-Time Markov Chains and Applications A Singular Perturbation Approach by G. George Yin, Qing Zhang New York, NY Springer New York 1998 1 Online-Ressource (XV, 351 p) txt rdacontent c rdamedia cr rdacarrier Applications of Mathematics, Stochastic Modelling and Applied Probability 37 0172-4568 This book is concerned with continuous-time Markov chains. It develops an integrated approach to singularly perturbed Markovian systems, and reveals interrelations of stochastic processes and singular perturbations. In recent years, Markovian formulations have been used routinely for nu merous real-world systems under uncertainties. Quite often, the underlying Markov chain is subject to rather frequent fluctuations and the correspond ing states are naturally divisible to a number of groups such that the chain fluctuates very rapidly among different states within a group, but jumps less frequently from one group to another. Various applications in engineer ing, economics, and biological and physical sciences have posed increasing demands on an in-depth study of such systems. A basic issue common to many different fields is the understanding of the distribution and the struc ture of the underlying uncertainty. Such needs become even more pressing when we deal with complex and/or large-scale Markovian models, whose closed-form solutions are usually very difficult to obtain. Markov chain, a well-known subject, has been studied by a host of re searchers for many years. While nonstationary cases have been treated in the literature, much emphasis has been on stationary Markov chains and their basic properties such as ergodicity, recurrence, and stability. In contrast, this book focuses on singularly perturbed nonstationary Markov chains and their asymptotic properties. Singular perturbation theory has a long history and is a powerful tool for a wide variety of applications Mathematics Mathematical optimization Distribution (Probability theory) Probability Theory and Stochastic Processes Calculus of Variations and Optimal Control; Optimization Mathematik Markov-Kette mit stetiger Zeit (DE-588)4272650-5 gnd rswk-swf Singuläre Störung (DE-588)4055100-3 gnd rswk-swf Markov-Kette mit stetiger Zeit (DE-588)4272650-5 s Singuläre Störung (DE-588)4055100-3 s 1\p DE-604 Zhang, Qing Sonstige oth https://doi.org/10.1007/978-1-4612-0627-9 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Yin, G. George Continuous-Time Markov Chains and Applications A Singular Perturbation Approach Mathematics Mathematical optimization Distribution (Probability theory) Probability Theory and Stochastic Processes Calculus of Variations and Optimal Control; Optimization Mathematik Markov-Kette mit stetiger Zeit (DE-588)4272650-5 gnd Singuläre Störung (DE-588)4055100-3 gnd |
| subject_GND | (DE-588)4272650-5 (DE-588)4055100-3 |
| title | Continuous-Time Markov Chains and Applications A Singular Perturbation Approach |
| title_auth | Continuous-Time Markov Chains and Applications A Singular Perturbation Approach |
| title_exact_search | Continuous-Time Markov Chains and Applications A Singular Perturbation Approach |
| title_full | Continuous-Time Markov Chains and Applications A Singular Perturbation Approach by G. George Yin, Qing Zhang |
| title_fullStr | Continuous-Time Markov Chains and Applications A Singular Perturbation Approach by G. George Yin, Qing Zhang |
| title_full_unstemmed | Continuous-Time Markov Chains and Applications A Singular Perturbation Approach by G. George Yin, Qing Zhang |
| title_short | Continuous-Time Markov Chains and Applications |
| title_sort | continuous time markov chains and applications a singular perturbation approach |
| title_sub | A Singular Perturbation Approach |
| topic | Mathematics Mathematical optimization Distribution (Probability theory) Probability Theory and Stochastic Processes Calculus of Variations and Optimal Control; Optimization Mathematik Markov-Kette mit stetiger Zeit (DE-588)4272650-5 gnd Singuläre Störung (DE-588)4055100-3 gnd |
| topic_facet | Mathematics Mathematical optimization Distribution (Probability theory) Probability Theory and Stochastic Processes Calculus of Variations and Optimal Control; Optimization Mathematik Markov-Kette mit stetiger Zeit Singuläre Störung |
| url | https://doi.org/10.1007/978-1-4612-0627-9 |
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