Cantitate/Preț
Produs

Stochastic Partial Differential Equations: A Modeling, White Noise Functional Approach: Probability and Its Applications

Autor Helge Holden, Bernt Oksendal, Jan Uboe, Tusheng Zhang
en Limba Engleză Hardback – aug 1996
This book is based on research that, to a large extent, started around 1990, when a research project on fluid flow in stochastic reservoirs was initiated by a group including some of us with the support of VISTA, a research coopera­ tion between the Norwegian Academy of Science and Letters and Den norske stats oljeselskap A.S. (Statoil). The purpose of the project was to use stochastic partial differential equations (SPDEs) to describe the flow of fluid in a medium where some of the parameters, e.g., the permeability, were stochastic or "noisy". We soon realized that the theory of SPDEs at the time was insufficient to handle such equations. Therefore it became our aim to develop a new mathematically rigorous theory that satisfied the following conditions. 1) The theory should be physically meaningful and realistic, and the corre­ sponding solutions should make sense physically and should be useful in applications. 2) The theory should be general enough to handle many of the interesting SPDEs that occur in reservoir theory and related areas. 3) The theory should be strong and efficient enough to allow us to solve th,~se SPDEs explicitly, or at least provide algorithms or approximations for the solutions.
Citește tot Restrânge

Toate formatele și edițiile

Toate formatele și edițiile Preț Express
Paperback (1) 92321 lei  43-57 zile
  Birkhäuser Boston – 16 iun 2012 92321 lei  43-57 zile
Hardback (1) 92907 lei  43-57 zile
  Birkhäuser Boston – aug 1996 92907 lei  43-57 zile

Din seria Probability and Its Applications

Preț: 92907 lei

Preț vechi: 113301 lei
-18% Nou

Puncte Express: 1394

Preț estimativ în valută:
17780 18469$ 14769£

Carte tipărită la comandă

Livrare economică 03-17 februarie 25

Preluare comenzi: 021 569.72.76

Specificații

ISBN-13: 9780817639280
ISBN-10: 0817639284
Pagini: 231
Ilustrații: XII, 231 p.
Dimensiuni: 156 x 234 x 16 mm
Greutate: 0.53 kg
Ediția:1996
Editura: Birkhäuser Boston
Colecția Birkhäuser
Seria Probability and Its Applications

Locul publicării:Boston, MA, United States

Public țintă

Research

Cuprins

1. Introduction.- 1.1. Modeling by stochastic differential equations.- 2. Framework.- 2.1. White noise.- 2.2. The Wiener-Itô chaos expansion.- 2.3. Stochastic test functions and stochastic distributions.- 2.4. The Wick product.- 2.5. Wick multiplication and Itô/Skorohod integration.- 2.6. The Hermite transform.- 2.7. The S)p,rN spaces and the S-transform.- 2.8. The topology of (S)-1N.- 2.9. The F-transform and the Wick product on L1 (?).- 2.10. The Wick product and translation.- 2.11. Positivity.- 3. Applications to stochastic ordinary differential equations.- 3.1. Linear equations.- 3.2. A model for population growth in a crowded stochastic environment.- 3.3. A general existence and uniqueness theorem.- 3.4. The stochastic Volterra equation.- 3.5. Wick products versus ordinary products: A comparison experiment Variance properties.- 3.6. Solution and Wick approximation of quasilinear SDE.- 4. Stochastic partial differential equations.- 4.1. General remarks.- 4.2. The stochastic Poisson equation.- 4.3. The stochastic transport equation.- 4.4. The stochastic Schrödinger equation.- 4.5. The viscous Burgers’ equation with a stochastic source.- 4.6. The stochastic pressure equation.- 4.7. The heat equation in a stochastic, anisotropic medium.- 4.8. A class of quasilinear parabolic SPDEs.- 4.9. SPDEs driven by Poissonian noise.- Appendix A. The Bochner-Minlos theorem.- Appendix B. A brief review of Itô calculus.- The Itô formula.- Stochastic differential equations.- The Girsanov theorem.- Appendix C. Properties of Hermite polynomials.- Appendix D. Independence of bases in Wick products.- References.- List of frequently used notation and symbols.

Recenzii

"The authors have made significant contributions to each of the areas. As a whole, the book is well organized and very carefully written and the details of the proofs are basically spelled out... This is a rich and demanding book… It will be of great value for students of probability theory or SPDEs with an interest in the subject, and also for professional probabilists."   —Mathematical Reviews
"...a comprehensive introduction to stochastic partial differential equations."   —Zentralblatt MATH
"This book will be invaluable to anyone interested in doing research in white noise theory or in applying this theory to solving real-world problems."   Computing Reviews