Introduction to stochastic processes using R:
This textbook presents some basic stochastic processes, mainly Markov processes. It begins with a brief introduction to the framework of stochastic processes followed by the thorough discussion on Markov chains, which is the simplest and the most important class of stochastic processes. The book the...
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| Format: | Buch |
| Sprache: | English |
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Singapore, Singapore
Springer
[2023]
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| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | This textbook presents some basic stochastic processes, mainly Markov processes. It begins with a brief introduction to the framework of stochastic processes followed by the thorough discussion on Markov chains, which is the simplest and the most important class of stochastic processes. The book then elaborates the theory of Markov chains in detail including classification of states, the first passage distribution, the concept of periodicity and the limiting behaviour of a Markov chain in terms of associated stationary and long run distributions. The book first illustrates the theory for some typical Markov chains, such as random walk, gambler's ruin problem, Ehrenfest model and Bienayme-Galton-Watson branching process; and then extends the discussion when time parameter is continuous. It presents some important examples of a continuous time Markov chain, which include Poisson process, birth process, death process, birth and death processes and their variations. These processesplay a fundamental role in the theory and applications in queuing and inventory models, population growth, epidemiology and engineering systems. The book studies in detail the Poisson process, which is the most frequently applied stochastic process in a variety of fields, with its extension to a renewal process.The book also presents important basic concepts on Brownian motion process, a stochastic process of historic importance. It covers its few extensions and variations, such as Brownian bridge, geometric Brownian motion process, which have applications in finance, stock markets, inventory etc. The book is designed primarily to serve as a textbook for a one semester introductory course in stochastic processes, in a post-graduate program, such as Statistics, Mathematics, Data Science and Finance. It can also be used for relevant courses in other disciplines. Additionally, it provides sufficient background material for studying inference in stochastic processes. The book thus fulfils the need of a concise but clear and student-friendly introduction to various types of stochastic processes |
| Beschreibung: | Basics of Stochastic Processes.- Markov Chains.- Long-run Behaviour of Markov Chains.- Random Walks.- Bienayme Galton Watson Branching Process.- Continuous Time Markov Chains.- Poisson Process.- Birth and Death Processes.- Brownian Motion Process.- Renewal Process.- Solutions Conceptual Exercises |
| Beschreibung: | xx, 651 Seiten Illustrationen, Diagramme 235 mm |
| ISBN: | 9789819956036 |
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| 520 | |a This textbook presents some basic stochastic processes, mainly Markov processes. It begins with a brief introduction to the framework of stochastic processes followed by the thorough discussion on Markov chains, which is the simplest and the most important class of stochastic processes. The book then elaborates the theory of Markov chains in detail including classification of states, the first passage distribution, the concept of periodicity and the limiting behaviour of a Markov chain in terms of associated stationary and long run distributions. The book first illustrates the theory for some typical Markov chains, such as random walk, gambler's ruin problem, Ehrenfest model and Bienayme-Galton-Watson branching process; and then extends the discussion when time parameter is continuous. It presents some important examples of a continuous time Markov chain, which include Poisson process, birth process, death process, birth and death processes and their variations. | ||
| 520 | |a These processesplay a fundamental role in the theory and applications in queuing and inventory models, population growth, epidemiology and engineering systems. The book studies in detail the Poisson process, which is the most frequently applied stochastic process in a variety of fields, with its extension to a renewal process.The book also presents important basic concepts on Brownian motion process, a stochastic process of historic importance. It covers its few extensions and variations, such as Brownian bridge, geometric Brownian motion process, which have applications in finance, stock markets, inventory etc. The book is designed primarily to serve as a textbook for a one semester introductory course in stochastic processes, in a post-graduate program, such as Statistics, Mathematics, Data Science and Finance. It can also be used for relevant courses in other disciplines. Additionally, it provides sufficient background material for studying inference in stochastic processes. | ||
| 520 | |a The book thus fulfils the need of a concise but clear and student-friendly introduction to various types of stochastic processes | ||
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Contents Basics of Stochastic Processes . 1.1 Introduction . 1.2 Kolmogorov CompatibilityConditions . 1.3 Stochastic Processes with Stationary and Independent Increments . 1.4 Stationary Processes . 1.5 Introduction to R Software and Language . References . 12 19 21 29 2 Markov Chains . 2.1 Introduction . 2.2 Higher Step Transition Probabilities. 2.3 Realization of a Markov Chain . 2.4 Classification of States . 2.5 Persistent and Transient States . 2.6 First Passage Distribution. 2.7 Periodicity . 2.8 R Codes. 2.9 Conceptual Exercises
. 2.10 Computational Exercises . 2.11 Multiple Choice Questions . References . 31 31 45 58 63 71 85 109 118 131 134 137 152 3 Long Run Behavior of Markov Chains . 3.1 Introduction . 3.2 Long Run Distribution . 3.3 Stationary Distribution . 3.4 Computation of Stationary Distributions . 3.5 Autocovariance Function . 3.6 Bonus-Malus System . 155 155 159 177 194 205 207 1 1 1 5 xi
xii Contents 3.7 R Codes. 3.8 Conceptual Exercises . 3.9 Computational Exercises . 3.10 Multiple Choice Questions . References . 209 214 217 219 223 4 Random Walks . 4.1 Introduction . 4.2 Random Walk with Countably Infinite State Space . 4.3 Random Walk with Finite State Space . 4.4 Gambler’s Ruin Problem . 4.5 Ehrenfest Chain and Birth-Death Chain. 4.6 R Codes. 4.7 Conceptual Exercises . 4.8 Computàtional Exercises . 4.9 Multiple Choice Questions . References . 225 225 226 239 243
252 256 262 263 264 271 5 Bienayme Galton WatsonBranching Process . 5.1 Introduction . 5.2 Markov Property . 5.3 Branching Property. 5.4 Extinction Probability . . 5.5 Realization of a Process and Computation of Extinction Probability . 5.6 RCodes. 5.7 Conceptual Exercises . 5.8 Computational Exercises . 5.9 Multiple Choice Questions . References . 273 273 279 283 288 297 304 314 315 316 320 Continuous Time Markov Chains. 6.1 Introduction . 6.2 Definition and Properties . :. 6.3 Transition Probability Function. 6.4 Infinitesimal
Generator. 6.5 Computation of Transition Probability Function . 6.6 Long Run Behavior. 6.7 R Codes. . . 6.8 Conceptual Exercises . 6.9 Computational Exercises . 6.10 Multiple Choice Questions . References . 321 321 325 332 343 351 362 373 381 383 384 387 6
Contents xiii 389 389 Poisson Process . 7.1 Introduction . 7.2 Poisson Process as a Process with Stationary and Independent Increments . 391 7.3 Poisson Process as a Point Process. 7.4 Non-homogeneous Poisson Process . 7.5 Superposition and Decomposition . 7.6 Compound Poisson Process. 7.7 R Codes. 7.8 Conceptual Exercises . 7.9 Computational Exercises . 7.10 Multiple Choice Questions . References . 408 415 416 421 428 434 437 437 440 8 Birth and Death Process . 8.1 Introduction . 8.2 Birth Process . 8.3 Death Process . 8.4 Birth-Death
Process . 8.5 Linear Birth-Death Process . 8.6 Long Run Behavior of a Birth-Death Process. 8.7 R Codes. 8.8 Conceptual Exercises . 8.9 Computational Exercises . 8.10 Multiple Choice Questions . References . 441 441 442 455 462 465 469 473 481 483 483 485 9 Brownian Motion Process. 9.1 Introduction . 9.2 Definition and Properties . 9.3 Realization and Properties of Sample Path . 9.4 Brownian Bridge . 9.5 Geometric Brownian Motion Process. 9.6 Variations of a Brownian Motion Process . 9.7 R Codes. 9.8 Conceptual Exercises . 9.9
Computational Exercises . 9.10 Multiple Choice Questions . References . 487 487 489 499 511 518 525 527 534 535 536 544 10 Renewal Process . 10.1 Introduction . 10.2 Renewal Function . 10.3 Long Run Renewal Rate. 10.4 Limit Theorems. 10.5 Generalizations and Variations of Renewal Processes . 547 547 551 558 562 568 7
Contents xiv 10.6 R Codes. 10.7 Conceptual Exercises . 10.8 Computational Exercises . 10.9 Multiple Choice Questions . References . 573 577 578 578 581 Appendix A: Solutions to Conceptual Exercises . 583 Index. 649 |
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| spelling | Madhira, Sivaprasad Verfasser aut Introduction to stochastic processes using R Sivaprasad Madhira, Shailaja Deshmukh Singapore, Singapore Springer [2023] xx, 651 Seiten Illustrationen, Diagramme 235 mm txt rdacontent n rdamedia nc rdacarrier Basics of Stochastic Processes.- Markov Chains.- Long-run Behaviour of Markov Chains.- Random Walks.- Bienayme Galton Watson Branching Process.- Continuous Time Markov Chains.- Poisson Process.- Birth and Death Processes.- Brownian Motion Process.- Renewal Process.- Solutions Conceptual Exercises This textbook presents some basic stochastic processes, mainly Markov processes. It begins with a brief introduction to the framework of stochastic processes followed by the thorough discussion on Markov chains, which is the simplest and the most important class of stochastic processes. The book then elaborates the theory of Markov chains in detail including classification of states, the first passage distribution, the concept of periodicity and the limiting behaviour of a Markov chain in terms of associated stationary and long run distributions. The book first illustrates the theory for some typical Markov chains, such as random walk, gambler's ruin problem, Ehrenfest model and Bienayme-Galton-Watson branching process; and then extends the discussion when time parameter is continuous. It presents some important examples of a continuous time Markov chain, which include Poisson process, birth process, death process, birth and death processes and their variations. These processesplay a fundamental role in the theory and applications in queuing and inventory models, population growth, epidemiology and engineering systems. The book studies in detail the Poisson process, which is the most frequently applied stochastic process in a variety of fields, with its extension to a renewal process.The book also presents important basic concepts on Brownian motion process, a stochastic process of historic importance. It covers its few extensions and variations, such as Brownian bridge, geometric Brownian motion process, which have applications in finance, stock markets, inventory etc. The book is designed primarily to serve as a textbook for a one semester introductory course in stochastic processes, in a post-graduate program, such as Statistics, Mathematics, Data Science and Finance. It can also be used for relevant courses in other disciplines. Additionally, it provides sufficient background material for studying inference in stochastic processes. The book thus fulfils the need of a concise but clear and student-friendly introduction to various types of stochastic processes Stochastic processes Probabilities Markov processes Econometrics Brownsche Bewegung (DE-588)4128328-4 gnd rswk-swf R Programm (DE-588)4705956-4 gnd rswk-swf Poisson-Prozess (DE-588)4174971-6 gnd rswk-swf Markov-Kette (DE-588)4037612-6 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Hardcover, Softcover / Wirtschaft/Volkswirtschaft Stochastischer Prozess (DE-588)4057630-9 s Markov-Kette (DE-588)4037612-6 s Poisson-Prozess (DE-588)4174971-6 s Brownsche Bewegung (DE-588)4128328-4 s R Programm (DE-588)4705956-4 s DE-604 Deshmukh, Shailaja Verfasser (DE-588)1089598947 aut Erscheint auch als Online-Ausgabe 978-981-99-5601-2 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=035395922&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Madhira, Sivaprasad Deshmukh, Shailaja Introduction to stochastic processes using R Stochastic processes Probabilities Markov processes Econometrics Brownsche Bewegung (DE-588)4128328-4 gnd R Programm (DE-588)4705956-4 gnd Poisson-Prozess (DE-588)4174971-6 gnd Markov-Kette (DE-588)4037612-6 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
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| title | Introduction to stochastic processes using R |
| title_auth | Introduction to stochastic processes using R |
| title_exact_search | Introduction to stochastic processes using R |
| title_full | Introduction to stochastic processes using R Sivaprasad Madhira, Shailaja Deshmukh |
| title_fullStr | Introduction to stochastic processes using R Sivaprasad Madhira, Shailaja Deshmukh |
| title_full_unstemmed | Introduction to stochastic processes using R Sivaprasad Madhira, Shailaja Deshmukh |
| title_short | Introduction to stochastic processes using R |
| title_sort | introduction to stochastic processes using r |
| topic | Stochastic processes Probabilities Markov processes Econometrics Brownsche Bewegung (DE-588)4128328-4 gnd R Programm (DE-588)4705956-4 gnd Poisson-Prozess (DE-588)4174971-6 gnd Markov-Kette (DE-588)4037612-6 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| topic_facet | Stochastic processes Probabilities Markov processes Econometrics Brownsche Bewegung R Programm Poisson-Prozess Markov-Kette Stochastischer Prozess |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=035395922&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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