An Introduction to Singular Stochastic PDEs
Author | : Nils Berglund |
Publisher | : |
Total Pages | : |
Release | : 2022 |
Genre | : |
ISBN | : 9783985470143 |
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Author | : Nils Berglund |
Publisher | : |
Total Pages | : |
Release | : 2022 |
Genre | : |
ISBN | : 9783985470143 |
Author | : Gabriel J. Lord |
Publisher | : Cambridge University Press |
Total Pages | : 516 |
Release | : 2014-08-11 |
Genre | : Business & Economics |
ISBN | : 0521899907 |
This book offers a practical presentation of stochastic partial differential equations arising in physical applications and their numerical approximation.
Author | : Andreas Eberle |
Publisher | : Springer |
Total Pages | : 574 |
Release | : 2018-07-03 |
Genre | : Mathematics |
ISBN | : 3319749293 |
This Festschrift contains five research surveys and thirty-four shorter contributions by participants of the conference ''Stochastic Partial Differential Equations and Related Fields'' hosted by the Faculty of Mathematics at Bielefeld University, October 10–14, 2016. The conference, attended by more than 140 participants, including PostDocs and PhD students, was held both to honor Michael Röckner's contributions to the field on the occasion of his 60th birthday and to bring together leading scientists and young researchers to present the current state of the art and promising future developments. Each article introduces a well-described field related to Stochastic Partial Differential Equations and Stochastic Analysis in general. In particular, the longer surveys focus on Dirichlet forms and Potential theory, the analysis of Kolmogorov operators, Fokker–Planck equations in Hilbert spaces, the theory of variational solutions to stochastic partial differential equations, singular stochastic partial differential equations and their applications in mathematical physics, as well as on the theory of regularity structures and paracontrolled distributions. The numerous research surveys make the volume especially useful for graduate students and researchers who wish to start work in the above-mentioned areas, or who want to be informed about the current state of the art.
Author | : Robert C. Dalang |
Publisher | : Springer Science & Business Media |
Total Pages | : 230 |
Release | : 2009 |
Genre | : Mathematics |
ISBN | : 3540859934 |
This title contains lectures that offer an introduction to modern topics in stochastic partial differential equations and bring together experts whose research is centered on the interface between Gaussian analysis, stochastic analysis, and stochastic PDEs.
Author | : Helge Holden |
Publisher | : Springer Science & Business Media |
Total Pages | : 312 |
Release | : 2009-12-01 |
Genre | : Mathematics |
ISBN | : 0387894888 |
The first edition of Stochastic Partial Differential Equations: A Modeling, White Noise Functional Approach, gave a comprehensive introduction to SPDEs. In this, the 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. The stochastic pressure equation for fluid flow in porous media is treated, as are applications to finance. Graduate students in pure and applied mathematics as well as researchers in SPDEs, physics, and engineering will find this introduction indispensible. Useful exercises are collected at the end of each chapter.
Author | : Boling Guo |
Publisher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 228 |
Release | : 2016-11-21 |
Genre | : Mathematics |
ISBN | : 3110493888 |
This book explains mathematical theories of a collection of stochastic partial differential equations and their dynamical behaviors. Based on probability and stochastic process, the authors discuss stochastic integrals, Ito formula and Ornstein-Uhlenbeck processes, and introduce theoretical framework for random attractors. With rigorous mathematical deduction, the book is an essential reference to mathematicians and physicists in nonlinear science. Contents: Preliminaries The stochastic integral and Itô formula OU processes and SDEs Random attractors Applications Bibliography Index
Author | : Simo Särkkä |
Publisher | : Cambridge University Press |
Total Pages | : 327 |
Release | : 2019-05-02 |
Genre | : Business & Economics |
ISBN | : 1316510085 |
With this hands-on introduction readers will learn what SDEs are all about and how they should use them in practice.
Author | : Wang Wei |
Publisher | : World Scientific |
Total Pages | : 240 |
Release | : 2019-05-07 |
Genre | : Mathematics |
ISBN | : 981120036X |
This volume is devoted to original research results and survey articles reviewing recent developments in reduction for stochastic PDEs with multiscale as well as application to science and technology, and to present some future research direction. This volume includes a dozen chapters by leading experts in the area, with a broad audience in mind. It should be accessible to graduate students, junior researchers and other professionals who are interested in the subject. We also take this opportunity to celebrate the contributions of Professor Anthony J Roberts, an internationally leading figure on the occasion of his 60th years birthday in 2017.
Author | : Wei Liu |
Publisher | : |
Total Pages | : |
Release | : 2015 |
Genre | : |
ISBN | : 9783319223551 |
This book provides an introduction to the theory of stochastic partial differential equations (SPDEs) of evolutionary type. SPDEs are one of the main research directions in probability theory with several wide ranging applications. Many types of dynamics with stochastic influence in nature or man-made complex systems can be modelled by such equations. The theory of SPDEs is based both on the theory of deterministic partial differential equations, as well as on modern stochastic analysis. Whilst this volume mainly follows the 'variational approach', it also contains a short account on the 'semigroup (or mild solution) approach'. In particular, the volume contains a complete presentation of the main existence and uniqueness results in the case of locally monotone coefficients. Various types of generalized coercivity conditions are shown to guarantee non-explosion, but also a systematic approach to treat SPDEs with explosion in finite time is developed. It is, so far, the only book where the latter and the 'locally monotone case' is presented in a detailed and complete way for SPDEs. The extension to this more general framework for SPDEs, for example, in comparison to the well-known case of globally monotone coefficients, substantially widens the applicability of the results. In addition, it leads to a unified approach and to simplified proofs in many classical examples. These include a large number of SPDEs not covered by the 'globally monotone case', such as, for exa mple, stochastic Burgers or stochastic 2D and 3D Navier-Stokes equations, stochastic Cahn-Hilliard equations and stochastic surface growth models. To keep the book self-contained and prerequisites low, necessary results about SDEs in finite dimensions are also included with complete proofs as well as a chapter on stochastic integration on Hilbert spaces. Further fundamentals (for example, a detailed account on the Yamada-Watanabe theorem in infinite dimensions) used in the book have added proofs in the appendix. The book can be used as a textbook for a one-year graduate course.
Author | : Giuseppe Da Prato |
Publisher | : Chapman & Hall/CRC |
Total Pages | : |
Release | : 2017-08-09 |
Genre | : |
ISBN | : 9781138417519 |
Stochastic Partial Differential Equations and Applications gives an overview of current state-of-the-art stochastic PDEs in several fields, such as filtering theory, stochastic quantization, quantum probability, and mathematical finance. Featuring contributions from leading expert participants at an international conference on the subject, this book presents valuable information for PhD students in probability and PDEs as well as for researchers in pure and applied mathematics. Coverage includes Navier-Stokes equations, Ornstein-Uhlenbeck semigroups, quantum stochastic differential equations, applications of SPDE, 3D stochastic Navier-Stokes equations, and nonlinear filtering.