Stochastic Equations in Infinite Dimensions
Seiten
2008
Cambridge University Press (Verlag)
978-0-521-05980-0 (ISBN)
Cambridge University Press (Verlag)
978-0-521-05980-0 (ISBN)
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The aim of this book is to give a systematic and self-contained presentation of basic results on stochastic evolution equations in infinite dimensional spaces.
The aim of this book is to give a systematic and self-contained presentation of basic results on stochastic evolution equations in infinite dimensional, typically Hilbert and Banach, spaces. These are a generalization of stochastic differential equations as introduced by Itô and Gikham that occur, for instance, when describing random phenomena that crop up in science and engineering, as well as in the study of differential equations. The book is divided into three parts. In the first the authors give a self-contained exposition of the basic properties of probability measure on separable Banach and Hilbert spaces, as required later; they assume a reasonable background in probability theory and finite dimensional stochastic processes. The second part is devoted to the existence and uniqueness of solutions of a general stochastic evolution equation, and the third concerns the qualitative properties of those solutions. Appendices gather together background results from analysis that are otherwise hard to find under one roof. The book ends with a comprehensive bibliography that will contribute to the book's value for all working in stochastic differential equations.
The aim of this book is to give a systematic and self-contained presentation of basic results on stochastic evolution equations in infinite dimensional, typically Hilbert and Banach, spaces. These are a generalization of stochastic differential equations as introduced by Itô and Gikham that occur, for instance, when describing random phenomena that crop up in science and engineering, as well as in the study of differential equations. The book is divided into three parts. In the first the authors give a self-contained exposition of the basic properties of probability measure on separable Banach and Hilbert spaces, as required later; they assume a reasonable background in probability theory and finite dimensional stochastic processes. The second part is devoted to the existence and uniqueness of solutions of a general stochastic evolution equation, and the third concerns the qualitative properties of those solutions. Appendices gather together background results from analysis that are otherwise hard to find under one roof. The book ends with a comprehensive bibliography that will contribute to the book's value for all working in stochastic differential equations.
Part I. Foundations: 1. Random variables; 2. Probability measures; 3. Stochastic processes; 4. The stochastic integral; Part II. Existence and Uniqueness: 5. Linear equations with additive noise; 6. Linear equations with multiplicative noise; 7. Existence and uniqueness for nonlinear equations; 8. Martingale solutions; Part III. Properties of Solutions: 9. Markov properties and Kolmogorov equations; 10. Absolute continuity and Girsanov's theorem; 11. Large time behaviour of solutions; 12. Small noise asymptotic.
| Erscheint lt. Verlag | 4.2.2008 |
|---|---|
| Reihe/Serie | Encyclopedia of Mathematics and its Applications |
| Verlagsort | Cambridge |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Gewicht | 668 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik | |
| ISBN-10 | 0-521-05980-1 / 0521059801 |
| ISBN-13 | 978-0-521-05980-0 / 9780521059800 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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