TY - BOOK UR - http://lib.ugent.be/catalog/ebk01:2560000000080609 ID - ebk01:2560000000080609 LA - eng TI - Markov Processes from K. Ito's Perspective (AM-155) PY - 2003 SN - 9781400835577 AU - Stroock, Daniel W., author. AB - Kiyosi Itô's greatest contribution to probability theory may be his introduction of stochastic differential equations to explain the Kolmogorov-Feller theory of Markov processes. Starting with the geometric ideas that guided him, this book gives an account of Itô's program. The modern theory of Markov processes was initiated by A. N. Kolmogorov. However, Kolmogorov's approach was too analytic to reveal the probabilistic foundations on which it rests. In particular, it hides the central role played by the simplest Markov processes: those with independent, identically distributed increments. To remedy this defect, Itô interpreted Kolmogorov's famous forward equation as an equation that describes the integral curve of a vector field on the space of probability measures. Thus, in order to show how Itô's thinking leads to his theory of stochastic integral equations, Stroock begins with an account of integral curves on the space of probability measures and then arrives at stochastic integral equations when he moves to a pathspace setting. In the first half of the book, everything is done in the context of general independent increment processes and without explicit use of Itô's stochastic integral calculus. In the second half, the author provides a systematic development of Itô's theory of stochastic integration: first for Brownian motion and then for continuous martingales. The final chapter presents Stratonovich's variation on Itô's theme and ends with an application to the characterization of the paths on which a diffusion is supported. The book should be accessible to readers who have mastered the essentials of modern probability theory and should provide such readers with a reasonably thorough introduction to continuous-time, stochastic processes. ER -Download RIS file
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020 | a 9781400835577 | ||
024 | 7 | a 10.1515/9781400835577 2 doi | |
035 | a (DE-B1597)447600 | ||
035 | a (OCoLC)888749095 | ||
040 | a IN-ChSCO b eng c IN-ChSCO e rda | ||
041 | a eng | ||
050 | 4 | a QA274.7 .S77 2003 | |
050 | 4 | a QA274.7 .S77 2003 b .S77 2003eb | |
072 | 7 | a MAT x 029040 2 bisacsh | |
072 | 7 | a MAT029040 2 bisacsh | |
082 | 4 | a 519.233 2 22 | |
082 | 4 | a 519.233 2 23 | |
100 | 1 | a Stroock, Daniel W., e author. | |
245 | 1 | a Markov Processes from K. Ito's Perspective (AM-155) / c Daniel W. Stroock. | |
264 | 1 | a Princeton, N.J. : b Princeton University Press, c [2003] | |
264 | 4 | c ©2003 | |
300 | a 1 online resource (288 pages) : b illustrations. | ||
336 | a text 2 rdacontent | ||
337 | a computer 2 rdamedia | ||
338 | a online resource 2 rdacarrier | ||
347 | a text file b PDF 2 rda | ||
490 | a Annals of Mathematics Studies, x 0066-2313 ; v 155 | ||
505 | t Frontmatter -- t Contents -- t Preface -- t Chapter 1. Finite State Space, a Trial Run -- t Chapter 2. Moving to Euclidean Space, the Real Thing -- t Chapter 3. Itô's Approach in the Euclidean Setting -- t Chapter 4. Further Considerations -- t Chapter 5. Itô's Theory of Stochastic Integration -- t Chapter 6. Applications of Stochastic Integration to Brownian Motion -- t Chapter 7. The Kunita-Watanabe Extension -- t Chapter 8. Stratonovich's Theory -- t Notation -- t References -- t Index. | ||
520 | a Kiyosi Itô's greatest contribution to probability theory may be his introduction of stochastic differential equations to explain the Kolmogorov-Feller theory of Markov processes. Starting with the geometric ideas that guided him, this book gives an account of Itô's program. The modern theory of Markov processes was initiated by A. N. Kolmogorov. However, Kolmogorov's approach was too analytic to reveal the probabilistic foundations on which it rests. In particular, it hides the central role played by the simplest Markov processes: those with independent, identically distributed increments. To remedy this defect, Itô interpreted Kolmogorov's famous forward equation as an equation that describes the integral curve of a vector field on the space of probability measures. Thus, in order to show how Itô's thinking leads to his theory of stochastic integral equations, Stroock begins with an account of integral curves on the space of probability measures and then arrives at stochastic integral equations when he moves to a pathspace setting. In the first half of the book, everything is done in the context of general independent increment processes and without explicit use of Itô's stochastic integral calculus. In the second half, the author provides a systematic development of Itô's theory of stochastic integration: first for Brownian motion and then for continuous martingales. The final chapter presents Stratonovich's variation on Itô's theme and ends with an application to the characterization of the paths on which a diffusion is supported. The book should be accessible to readers who have mastered the essentials of modern probability theory and should provide such readers with a reasonably thorough introduction to continuous-time, stochastic processes. | ||
533 | a Electronic reproduction. b Princeton, N.J. : c Princeton University Press, d 2003. n Mode of access: World Wide Web. n System requirements: Web browser. n Access may be restricted to users at subscribing institutions. | ||
538 | a Mode of access: Internet via World Wide Web. | ||
546 | a In English. | ||
588 | a Description based on online resource; title from PDF title page (publisher’s Web site, viewed October 27 2015) | ||
650 | a Markov processes. | ||
650 | a MATHEMATICS v Applied. | ||
650 | a MATHEMATICS v Probability & x Statistics v General. | ||
650 | a MATHEMATICS v Probability & x Statistics v Stochastic Processes. | ||
650 | a Stochastic integrals. | ||
650 | 4 | a Ito, Kiyosi, 1915-2008. | |
650 | 4 | a Markov processes. | |
650 | 4 | a Mathematics, other. | |
650 | 4 | a Mathematics. | |
650 | 4 | a Mathematik. | |
650 | 4 | a Stochastic difference equations. | |
650 | 4 | a Stochastic integrals. | |
773 | 8 | i Title is part of eBook package: d De Gruyter t Princeton Annals of Mathematics Backlist eBook Package z 978-3-11-049491-4 | |
773 | 8 | i Title is part of eBook package: d De Gruyter t Princeton eBook Package Backlist 2000-2013 z 978-3-11-044250-2 | |
773 | 8 | i Title is part of eBook package: d De Gruyter t Princeton eBook Package Backlist 2000-2014 z 978-3-11-045953-1 | |
773 | 8 | i Title is part of eBook package: d De Gruyter t Princeton Univ. Press eBook Package 2000-2013 z 978-3-11-041343-4 | |
830 | a Annals of Mathematics Studies ; v 155. | ||
856 | 4 | u https://doi.org/10.1515/9781400835577 | |
856 | 4 | 2 | 3 Cover u https://www.degruyter.com/doc/cover/9781400835577.jpg |
912 | a 978-3-11-041343-4 Princeton Univ. Press eBook Package 2000-2013 | ||
912 | a 978-3-11-044250-2 Princeton eBook Package Backlist 2000-2013 | ||
912 | a 978-3-11-045953-1 Princeton eBook Package Backlist 2000-2014 | ||
912 | a 978-3-11-049491-4 Princeton Annals of Mathematics Backlist eBook Package | ||
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