|Statement||Tadahisa Funaki, Wojbor A. Woyczynski, editors.|
|Series||The IMA volumes in mathematics and its applications ;, v. 77|
|Contributions||Funaki, Tadahisa., Woyczyński, W. A. 1943-|
|LC Classifications||QA274.25 .N66 1996|
|The Physical Object|
|Pagination||xviii, 312 p. :|
|Number of Pages||312|
|LC Control Number||95044888|
A vner Friedman Willard Miller, Jr. xiii PREFACE A workshop on Nonlinear Stochastic Partial Differential Equations was held during the week of March 21 at the Institute for Mathematics and Its Applications at the University of Minnesota. Since the first edition was published, there has been a surge of interest in stochastic partial differential equations (PDEs) driven by the Lévy type of noise. Stochastic Partial Differential Equations, Second Edition incorporates these recent developments and improves the presentation of : Hardcover. be fully nonlinear), we establish a complete theory, including global existence and comparison principle. Our methodology relies heavily on the method of characteristics. Key words: Stochastic PDEs, path-dependent PDEs, rough PDEs, rough paths, viscosity solutions, comparison principle, functional Itˆo formula, char-acteristics, rough Taylor. 'This book gives both accessible and extensive coverage on stochastic partial differential equations and their numerical solutions. It offers a well-elaborated background needed for solving numerically stochastic PDEs, both parabolic and by:
Member of the Institut Universitaire de France, Pardoux has published more than papers on nonlinear filtering, stochastic partial differential equations, anticipating stochastic calculus, backward stochastic differential equations, homogenization and probabilistic models in evolutionary biology, and three books. About this book This book is focused on the recent developments on problems of probability model uncertainty by using the notion of nonlinear expectations and, in particular, sublinear expectations. It provides a gentle coverage of the theory of nonlinear expectations and related stochastic : Springer-Verlag Berlin Heidelberg. Non-linear Partial Differential Equations, Introduction to Non-linear Partial Differential Equations, Viscosity Solution Method in Non-linear Stochastic Partial Differential Equations. scattering theory) for various nonlinear dispersive and wave equations, such as the Korteweg-de Vries (KdV), nonlinear Schr¨odinger, nonlinear wave, and wave maps equations. The theory here is rich and vast and we cannot hope to present a comprehensive survey of the ﬁeld here; our aim is instead to present a sample of.
We study a “new kind” of backward doubly stochastic differential equations, where the nonlinear noise term is given by Itô–Kunita's stochastic integral. This allows us to give a probabilistic interpretation of classical and Sobolev's solutions of semilinear parabolic stochastic partial differential equations driven by a nonlinear space Cited by: Stochastic partial differential equations (SPDEs) generalize partial differential equations via random force terms and coefficients, in the same way ordinary stochastic differential equations generalize ordinary differential equations. They have relevance to quantum field theory, statistical mechanics, and spatial modeling. Sergei Kuznetsov is one of the top experts on measure valued branching processes (also known as “superprocesses”) and their connection to nonlinear partial diﬀerential operators. His research interests range from stochastic processes and partial diﬀerential equations to Format: Hardcover. He then discusses a unified theory of stochastic evolution equations and describes a few applied problems, including the random vibration of a nonlinear elastic beam and invariant measures for stochastic Navier-Stokes equations. The book concludes by pointing out the connection of stochastic PDEs to infinite-dimensional stochastic analysis.