Stochastic Partial Differential Equations: A Modeling, White Noise Functional Approach (Universitext)
| Author | : | |
| Rating | : | 4.97 (598 Votes) |
| Asin | : | 038789487X |
| Format Type | : | paperback |
| Number of Pages | : | 305 Pages |
| Publish Date | : | 2017-05-28 |
| Language | : | English |
DESCRIPTION:
Helge Holden is a professor of mathematics at the Norwegian University of Science and Technology and an adjunt professor at the Center of Mathematics for Applications, part of the University of Oslo. He has done extensive research in stochastic analysis, in particular in its application to flow in porous media.Bernt Øksendal is a professor at the Center of Mathematics for Applications at the University of Oslo. He is a winner of the Nansen Prize for research in stochastic analysis and its applications.Jan Ubøe is a professor in the Department of Finance and Management Sciences at the Norwegian School of Economics and Business Administration. He has written many papers about this subject.Tusheng Zhang is a professor of probability at the University of Manchester. His current area of research is stochastic differential and partial differential equations, and he recently published a monograph on fractional Brownian fields with Bernt Øksendal and others.
Paul Thurston said Accessible Intro for Wick Products and Calculus on Hida space. The authors have prepared a very accessible introduction for elements of the Malliavin calculus, analysis on the Hida space, and the Wick product with applications to stochastic PDEs. This material is also a prerequisite for some of the new modeling theories which extend the classical SPDE models based on semimartingale diffusions to a more general setting. As an example of these extensions, see Mishura's Stochastic Calculus for Fractional Brownian Motion and Related Processes or the work of Biagini, Hu, Oksendal, and Zhang in Stochastic Calculus for Fractional Brownian Motion and Applications.The reader will need some prerequisites to ge. Great companion text to the "Malliavin Calculus for Levy Processes Rolando Navarro, Jr. Great companion text to the "Malliavin Calculus for Levy Processes with Applications to Finance" by Di Nunno, Oksendal, and Proske. This book is a must for researchers seriously doing research White Noise Malliavin Calculus in Finance.. Rama Cont said A new approach to stochastic partial differential equations. SUMMARY: This book presents a new approach to stochastic partial differential equations based on white noise analysis. The framework makes heavy use of functional analysis and its main starting point is the Wiener chaos expansion and analogous expansions on different functional spaces (Schwartz spaces).A stochastic PDE is a PDE containing a random noise term, which may be additive or multiplicative. One of the problems when working with Stochastic PDEs is to define a notion of solution which is meaningfully extendable to the nonlinear case. Problems arises because the noise term is highly irregular: for each sample of the noise, one has a
In this second edition, the authors build on the theory of SPDEs driven by space-time Brownian motion, or more generally, space-time Lévy process noise. Applications of the theory are emphasized throughout and useful exercises are at the end of each chapter.
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 applyin