Brownian Motion and Stochastic Calculus:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
New York ; Berlin ; Heidelberg ; London ; Paris ; Tokyo
Springer
1988
|
| Series: | Graduate Texts in Mathematics
113 |
| Subjects: | |
| Online Access: | UBM01 UPA01 UPA01 Volltext |
| Item Description: | Two of the most fundamental concepts in the theory of stochastic processes are the Markov property and the martingale property. * This book is written for readers who are acquainted with both of these ideas in the discrete-time setting, and who now wish to explore stochastic processes in their continuoustime context. It has been our goal to write a systematic and thorough exposition of this subject, leading in many instances to the frontiers of knowledge. At the same time, we have endeavored to keep the mathematical prerequisites as low as possible, namely, knowledge of measure-theoretic probability and some familiarity with discrete-time processes. The vehicle we have chosen for this task is Brownian motion, which we present as the canonical example of both a Markov process and a martingale. We support this point of view by showing how, by means of stochastic integration and random time change, all continuous-path martingales and a multitude of continuous-path Markov processes can be represented in terms of Brownian motion. This approach forces us to leave aside those processes which do not have continuous paths. Thus, the Poisson process is not a primary object of study, although it is developed in Chapter 1 to be used as a tool when we later study passage times and local time of Brownian motion |
| Physical Description: | 1 Online-Ressource (xxiii, 470 Seiten) |
| ISBN: | 9781468403022 |
| ISSN: | 0072-5285 |
| DOI: | 10.1007/978-1-4684-0302-2 |
Staff View
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| spelling | Karatzas, Ioannis 1952- Verfasser (DE-588)140840346 aut Brownian Motion and Stochastic Calculus Ioannis Karatzas, Steven E. Shreve New York ; Berlin ; Heidelberg ; London ; Paris ; Tokyo Springer 1988 1 Online-Ressource (xxiii, 470 Seiten) txt rdacontent c rdamedia cr rdacarrier Graduate Texts in Mathematics 113 0072-5285 Two of the most fundamental concepts in the theory of stochastic processes are the Markov property and the martingale property. * This book is written for readers who are acquainted with both of these ideas in the discrete-time setting, and who now wish to explore stochastic processes in their continuoustime context. It has been our goal to write a systematic and thorough exposition of this subject, leading in many instances to the frontiers of knowledge. At the same time, we have endeavored to keep the mathematical prerequisites as low as possible, namely, knowledge of measure-theoretic probability and some familiarity with discrete-time processes. The vehicle we have chosen for this task is Brownian motion, which we present as the canonical example of both a Markov process and a martingale. We support this point of view by showing how, by means of stochastic integration and random time change, all continuous-path martingales and a multitude of continuous-path Markov processes can be represented in terms of Brownian motion. This approach forces us to leave aside those processes which do not have continuous paths. Thus, the Poisson process is not a primary object of study, although it is developed in Chapter 1 to be used as a tool when we later study passage times and local time of Brownian motion Mathematics Distribution (Probability theory) Probability Theory and Stochastic Processes Mathematik Analyse stochastique Mouvement brownien, Processus de Processus stochastiques ram Brownian motion processes Stochastic analysis Stochastische Analysis (DE-588)4132272-1 gnd rswk-swf Brownsche Bewegung (DE-588)4128328-4 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Stochastik (DE-588)4121729-9 gnd rswk-swf Stetigkeit (DE-588)4183167-6 gnd rswk-swf Brownsche Bewegung (DE-588)4128328-4 s Stochastischer Prozess (DE-588)4057630-9 s DE-604 Stochastische Analysis (DE-588)4132272-1 s Stetigkeit (DE-588)4183167-6 s Stochastik (DE-588)4121729-9 s Shreve, Steven E. Verfasser aut Erscheint auch als Druck-Ausgabe 978-1-4684-0304-6 Erscheint auch als Druck-Ausgabe 3-540-96535-1 Graduate Texts in Mathematics 113 (DE-604)BV035421258 113 https://doi.org/10.1007/978-1-4684-0302-2 Verlag Volltext |
| spellingShingle | Karatzas, Ioannis 1952- Shreve, Steven E. Brownian Motion and Stochastic Calculus Graduate Texts in Mathematics Mathematics Distribution (Probability theory) Probability Theory and Stochastic Processes Mathematik Analyse stochastique Mouvement brownien, Processus de Processus stochastiques ram Brownian motion processes Stochastic analysis Stochastische Analysis (DE-588)4132272-1 gnd Brownsche Bewegung (DE-588)4128328-4 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Stochastik (DE-588)4121729-9 gnd Stetigkeit (DE-588)4183167-6 gnd |
| subject_GND | (DE-588)4132272-1 (DE-588)4128328-4 (DE-588)4057630-9 (DE-588)4121729-9 (DE-588)4183167-6 |
| title | Brownian Motion and Stochastic Calculus |
| title_auth | Brownian Motion and Stochastic Calculus |
| title_exact_search | Brownian Motion and Stochastic Calculus |
| title_full | Brownian Motion and Stochastic Calculus Ioannis Karatzas, Steven E. Shreve |
| title_fullStr | Brownian Motion and Stochastic Calculus Ioannis Karatzas, Steven E. Shreve |
| title_full_unstemmed | Brownian Motion and Stochastic Calculus Ioannis Karatzas, Steven E. Shreve |
| title_short | Brownian Motion and Stochastic Calculus |
| title_sort | brownian motion and stochastic calculus |
| topic | Mathematics Distribution (Probability theory) Probability Theory and Stochastic Processes Mathematik Analyse stochastique Mouvement brownien, Processus de Processus stochastiques ram Brownian motion processes Stochastic analysis Stochastische Analysis (DE-588)4132272-1 gnd Brownsche Bewegung (DE-588)4128328-4 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Stochastik (DE-588)4121729-9 gnd Stetigkeit (DE-588)4183167-6 gnd |
| topic_facet | Mathematics Distribution (Probability theory) Probability Theory and Stochastic Processes Mathematik Analyse stochastique Mouvement brownien, Processus de Processus stochastiques Brownian motion processes Stochastic analysis Stochastische Analysis Brownsche Bewegung Stochastischer Prozess Stochastik Stetigkeit |
| url | https://doi.org/10.1007/978-1-4684-0302-2 |
| volume_link | (DE-604)BV035421258 |
| work_keys_str_mv | AT karatzasioannis brownianmotionandstochasticcalculus AT shrevestevene brownianmotionandstochasticcalculus |