Stochastic analysis and diffusion processes:
Stochastic Analysis and Diffusion Processes presents a simple, mathematical introduction to Stochastic Calculus and its applications. The book builds the basic theory and offers a careful account of important research directions in Stochastic Analysis. The breadth and power of Stochastic Analysis, a...
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| Main Authors: | , |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Oxford
Oxford University Press
2014
|
| Edition: | First edition |
| Series: | Oxford graduate texts in mathematics
24 |
| Subjects: | |
| Online Access: | FAW01 FAW02 TUM01 UBT01 Volltext |
| Summary: | Stochastic Analysis and Diffusion Processes presents a simple, mathematical introduction to Stochastic Calculus and its applications. The book builds the basic theory and offers a careful account of important research directions in Stochastic Analysis. The breadth and power of Stochastic Analysis, and probabilistic behavior of diffusion processes are told without compromising on the mathematical details.Starting with the construction of stochastic processes, the book introduces Brownian motion and martingales. The book proceeds to construct stochastic integrals, establish the Ito formula, and discuss its applications. Next, attention is focused on stochastic differential equations (SDEs) which arise in modeling physical phenomena, perturbed by random forces. Diffusion processes are solutions of SDEs and form the main theme of this book.The Stroock-Varadhan martingale problem, the connection between diffusion processes and partial differential equations, Gaussian solutions of SDEs, and Markov processes with jumps are presented in successive chapters. The book culminates with a careful treatment of important research topics such as invariant measures, ergodic behavior, and large deviation principle for diffusions.Examples are given throughout the book to illustrate concepts and results. In addition, exercises are given at the end of each chapter that will help the reader to understand the concepts better. The book is written for graduate students, young researchers and applied scientists who are interested in stochastic processes and their applications. The reader is assumed to be familiar with probability theory at graduate level. The book can be used as a text for a graduate course on Stochastic Analysis |
| Physical Description: | 1 Online-Ressource (XI, 352 Seiten) |
| ISBN: | 9780191781759 |
| DOI: | 10.1093/acprof:oso/9780199657063.001.0001 |
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| indexdate | 2024-07-10T07:15:26Z |
| institution | BVB |
| isbn | 9780191781759 |
| language | English |
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| spelling | Kallianpur, Gopinath 1925- Verfasser (DE-588)119075547 aut Stochastic analysis and diffusion processes Gopinath Kallianpur and P. Sundar First edition Oxford Oxford University Press 2014 1 Online-Ressource (XI, 352 Seiten) txt rdacontent c rdamedia cr rdacarrier Oxford graduate texts in mathematics 24 Stochastic Analysis and Diffusion Processes presents a simple, mathematical introduction to Stochastic Calculus and its applications. The book builds the basic theory and offers a careful account of important research directions in Stochastic Analysis. The breadth and power of Stochastic Analysis, and probabilistic behavior of diffusion processes are told without compromising on the mathematical details.Starting with the construction of stochastic processes, the book introduces Brownian motion and martingales. The book proceeds to construct stochastic integrals, establish the Ito formula, and discuss its applications. Next, attention is focused on stochastic differential equations (SDEs) which arise in modeling physical phenomena, perturbed by random forces. Diffusion processes are solutions of SDEs and form the main theme of this book.The Stroock-Varadhan martingale problem, the connection between diffusion processes and partial differential equations, Gaussian solutions of SDEs, and Markov processes with jumps are presented in successive chapters. The book culminates with a careful treatment of important research topics such as invariant measures, ergodic behavior, and large deviation principle for diffusions.Examples are given throughout the book to illustrate concepts and results. In addition, exercises are given at the end of each chapter that will help the reader to understand the concepts better. The book is written for graduate students, young researchers and applied scientists who are interested in stochastic processes and their applications. The reader is assumed to be familiar with probability theory at graduate level. The book can be used as a text for a graduate course on Stochastic Analysis MATHEMATICS / Applied bisacsh MATHEMATICS / Probability & Statistics / General bisacsh Mathematics ukslc Diffusion processes fast Stochastic analysis fast Mathematik Diffusion processes Stochastic analysis Stochastische Analysis (DE-588)4132272-1 gnd rswk-swf Diffusionsprozess (DE-588)4274463-5 gnd rswk-swf Stochastische Analysis (DE-588)4132272-1 s Diffusionsprozess (DE-588)4274463-5 s DE-604 Sundar, Padmanabhan Verfasser (DE-588)1052297021 aut Erscheint auch als Druck-Ausgabe 978-0-19-965706-3 Oxford graduate texts in mathematics 24 (DE-604)BV045110902 24 https://doi.org/10.1093/acprof:oso/9780199657063.001.0001 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Kallianpur, Gopinath 1925- Sundar, Padmanabhan Stochastic analysis and diffusion processes Oxford graduate texts in mathematics MATHEMATICS / Applied bisacsh MATHEMATICS / Probability & Statistics / General bisacsh Mathematics ukslc Diffusion processes fast Stochastic analysis fast Mathematik Diffusion processes Stochastic analysis Stochastische Analysis (DE-588)4132272-1 gnd Diffusionsprozess (DE-588)4274463-5 gnd |
| subject_GND | (DE-588)4132272-1 (DE-588)4274463-5 |
| title | Stochastic analysis and diffusion processes |
| title_auth | Stochastic analysis and diffusion processes |
| title_exact_search | Stochastic analysis and diffusion processes |
| title_full | Stochastic analysis and diffusion processes Gopinath Kallianpur and P. Sundar |
| title_fullStr | Stochastic analysis and diffusion processes Gopinath Kallianpur and P. Sundar |
| title_full_unstemmed | Stochastic analysis and diffusion processes Gopinath Kallianpur and P. Sundar |
| title_short | Stochastic analysis and diffusion processes |
| title_sort | stochastic analysis and diffusion processes |
| topic | MATHEMATICS / Applied bisacsh MATHEMATICS / Probability & Statistics / General bisacsh Mathematics ukslc Diffusion processes fast Stochastic analysis fast Mathematik Diffusion processes Stochastic analysis Stochastische Analysis (DE-588)4132272-1 gnd Diffusionsprozess (DE-588)4274463-5 gnd |
| topic_facet | MATHEMATICS / Applied MATHEMATICS / Probability & Statistics / General Mathematics Diffusion processes Stochastic analysis Mathematik Stochastische Analysis Diffusionsprozess |
| url | https://doi.org/10.1093/acprof:oso/9780199657063.001.0001 |
| volume_link | (DE-604)BV045110902 |
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