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Markov Processes from K. Itô's Perspective (AM-155)
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 th...
| Autor principal: | |
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| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Princeton :
Princeton University Press,
2003.
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| Colección: | Book collections on Project MUSE.
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| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 020 | |a 9781400835577 | ||
| 020 | |z 9780691115436 | ||
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| 040 | |a MdBmJHUP |c MdBmJHUP | ||
| 100 | 1 | |a Stroock, Daniel W. | |
| 245 | 1 | 0 | |a Markov Processes from K. Itô's Perspective (AM-155) |
| 264 | 1 | |a Princeton : |b Princeton University Press, |c 2003. | |
| 264 | 3 | |a Baltimore, Md. : |b Project MUSE, |c 0000 | |
| 264 | 4 | |c ©2003. | |
| 300 | |a 1 online resource. | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 0 | |a Annals of Mathematics Studies | |
| 505 | 0 | 0 | |6 880-01 |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. | ||
| 546 | |a In English. | ||
| 588 | |a Description based on print version record. | ||
| 650 | 7 | |a Markov-Prozess |2 gnd | |
| 650 | 7 | |a Stochastic integrals. |2 fast |0 (OCoLC)fst01133512 | |
| 650 | 7 | |a Markov processes. |2 fast |0 (OCoLC)fst01010347 | |
| 650 | 7 | |a MATHEMATICS |x Probability & Statistics |x Stochastic Processes. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Probability & Statistics |x General. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Applied. |2 bisacsh | |
| 650 | 6 | |a Integrales stochastiques. | |
| 650 | 6 | |a Processus de Markov. | |
| 650 | 4 | |a Mathematical Statistics. | |
| 650 | 4 | |a Physical Sciences & Mathematics. | |
| 650 | 4 | |a Mathematics. | |
| 650 | 2 | |a Markov Chains | |
| 650 | 0 | |a Stochastic integrals. | |
| 650 | 0 | |a Markov processes. | |
| 655 | 7 | |a Electronic books. |2 local | |
| 710 | 2 | |a Project Muse. |e distributor | |
| 830 | 0 | |a Book collections on Project MUSE. | |
| 880 | 8 | |6 505-01/(S |a 1.3.4. The Markov Property and Kolmogorov''s Equations1.3.5. Exercises; 1.4 Pathspace Realization; 1.4.1. Kolmogorov''s Approach; 1.4.2. Levy Processes on Zn; 1.4.3. Exercises; 1.5 Itô''s Idea; 1.5.1. Itô''s Construction; 1.5.2. Exercises; 1.6 Another Approach; 1.6.1. Itô''s Approximation Scheme; 1.6.2. Exercises; Chapter 2 Moving to Euclidean Space, the Real Thing; 2.1 Tangent Vectors to M1(R^n); 2.1.1. Differentiable Curves on M1(R^n); 2.1.2. Infinitely Divisible Flows on M1(R^n); 2.1.3. The Tangent Space at δx; 2.1.4. The Tangent Space at General μ ∈ M1(R^n); 2.1.5. Exercises. | |
| 880 | 0 | |6 505-00/(S |a Cover; Title; Copyright; Dedication; Contents; Preface; Chapter 1 Finite State Space, a Trial Run; 1.1 An Extrinsic Perspective; 1.1.1. The Structure of Θn; 1.1.2. Back to M1(Zn); 1.2 A More Intrinsic Approach; 1.2.1. The Semigroup Structure on M1(Zn); 1.2.2. Infinitely Divisible Flows; 1.2.3. An Intrinsic Description of Tδx (M1(Zn)); 1.2.4. An Intrinsic Approach to (1.1.6); 1.2.5. Exercises; 1.3 Vector Fields and Integral Curves on M1(Zn); 1.3.1. Affine and Translation Invariant Vector Fields; 1.3.2. Existence of an Integral Curve; 1.3.3. Uniqueness for Affine Vector Fields. | |
| 856 | 4 | 0 | |z Texto completo |u https://projectmuse.uam.elogim.com/book/35289/ |
| 945 | |a Project MUSE - Custom Collection | ||