Download or read book Three Classes Of Nonlinear Stochastic Partial Differential Equations written by Jie Xiong and published by World Scientific. This book was released on 2013-05-06 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of measure-valued processes in random environments has seen some intensive research activities in recent years whereby interesting nonlinear stochastic partial differential equations (SPDEs) were derived. Due to the nonlinearity and the non-Lipschitz continuity of their coefficients, new techniques and concepts have recently been developed for the study of such SPDEs. These include the conditional Laplace transform technique, the conditional mild solution, and the bridge between SPDEs and some kind of backward stochastic differential equations. This volume provides an introduction to these topics with the aim of attracting more researchers into this exciting and young area of research. It can be considered as the first book of its kind. The tools introduced and developed for the study of measure-valued processes in random environments can be used in a much broader area of nonlinear SPDEs.
Download or read book A Concise Course on Stochastic Partial Differential Equations written by Claudia Prévôt and published by Springer. This book was released on 2007-05-26 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: These lectures concentrate on (nonlinear) stochastic partial differential equations (SPDE) of evolutionary type. There are three approaches to analyze SPDE: the "martingale measure approach", the "mild solution approach" and the "variational approach". The purpose of these notes is to give a concise and as self-contained as possible an introduction to the "variational approach". A large part of necessary background material is included in appendices.
Download or read book Nonlinear Partial Differential Equations with Applications written by Tomás Roubicek and published by Springer Science & Business Media. This book was released on 2006-01-17 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book primarily concerns quasilinear and semilinear elliptic and parabolic partial differential equations, inequalities, and systems. The exposition quickly leads general theory to analysis of concrete equations, which have specific applications in such areas as electrically (semi-) conductive media, modeling of biological systems, and mechanical engineering. Methods of Galerkin or of Rothe are exposed in a large generality.
Download or read book Nonlinear Stochastic Operator Equations written by George Adomian and published by Academic Press. This book was released on 2014-05-09 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear Stochastic Operator Equations deals with realistic solutions of the nonlinear stochastic equations arising from the modeling of frontier problems in many fields of science. This book also discusses a wide class of equations to provide modeling of problems concerning physics, engineering, operations research, systems analysis, biology, medicine. This text discusses operator equations and the decomposition method. This book also explains the limitations, restrictions and assumptions made in differential equations involving stochastic process coefficients (the stochastic operator case), which yield results very different from the needs of the actual physical problem. Real-world application of mathematics to actual physical problems, requires making a reasonable model that is both realistic and solvable. The decomposition approach or model is an approximation method to solve a wide range of problems. This book explains an inherent feature of real systems—known as nonlinear behavior—that occurs frequently in nuclear reactors, in physiological systems, or in cellular growth. This text also discusses stochastic operator equations with linear boundary conditions. This book is intended for students with a mathematics background, particularly senior undergraduate and graduate students of advanced mathematics, of the physical or engineering sciences.
Download or read book Stochastic Partial Differential Equations and Related Fields written by Andreas Eberle and published by Springer. This book was released on 2018-07-03 with total page 565 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Stochastic Ordinary and Stochastic Partial Differential Equations written by Peter Kotelenez and published by Springer Science & Business Media. This book was released on 2007-12-05 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic Partial Differential Equations analyzes mathematical models of time-dependent physical phenomena on microscopic, macroscopic and mesoscopic levels. It provides a rigorous derivation of each level from the preceding one and examines the resulting mesoscopic equations in detail. Coverage first describes the transition from the microscopic equations to the mesoscopic equations. It then covers a general system for the positions of the large particles.
Download or read book Stochastic Partial Differential Equations Second Edition written by Pao-Liu Chow and published by CRC Press. This book was released on 2014-12-10 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Explore Theory and Techniques to Solve Physical, Biological, and Financial Problems 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 material. New to the Second Edition Two sections on the Lévy type of stochastic integrals and the related stochastic differential equations in finite dimensions Discussions of Poisson random fields and related stochastic integrals, the solution of a stochastic heat equation with Poisson noise, and mild solutions to linear and nonlinear parabolic equations with Poisson noises Two sections on linear and semilinear wave equations driven by the Poisson type of noises Treatment of the Poisson stochastic integral in a Hilbert space and mild solutions of stochastic evolutions with Poisson noises Revised proofs and new theorems, such as explosive solutions of stochastic reaction diffusion equations Additional applications of stochastic PDEs to population biology and finance Updated section on parabolic equations and related elliptic problems in Gauss–Sobolev spaces The book covers basic theory as well as computational and analytical techniques to solve physical, biological, and financial problems. It first presents classical concrete problems before proceeding to a unified theory of stochastic evolution equations and describing applications, such as turbulence in fluid dynamics, a spatial population growth model in a random environment, and a stochastic model in bond market theory. The author also explores the connection of stochastic PDEs to infinite-dimensional stochastic analysis.
Download or read book A Minicourse on Stochastic Partial Differential Equations written by Robert C. Dalang and published by Springer Science & Business Media. This book was released on 2009 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Stochastic Differential Equations Backward SDEs Partial Differential Equations written by Etienne Pardoux and published by Springer. This book was released on 2014-06-24 with total page 680 pages. Available in PDF, EPUB and Kindle. Book excerpt: This research monograph presents results to researchers in stochastic calculus, forward and backward stochastic differential equations, connections between diffusion processes and second order partial differential equations (PDEs), and financial mathematics. It pays special attention to the relations between SDEs/BSDEs and second order PDEs under minimal regularity assumptions, and also extends those results to equations with multivalued coefficients. The authors present in particular the theory of reflected SDEs in the above mentioned framework and include exercises at the end of each chapter. Stochastic calculus and stochastic differential equations (SDEs) were first introduced by K. Itô in the 1940s, in order to construct the path of diffusion processes (which are continuous time Markov processes with continuous trajectories taking their values in a finite dimensional vector space or manifold), which had been studied from a more analytic point of view by Kolmogorov in the 1930s. Since then, this topic has become an important subject of Mathematics and Applied Mathematics, because of its mathematical richness and its importance for applications in many areas of Physics, Biology, Economics and Finance, where random processes play an increasingly important role. One important aspect is the connection between diffusion processes and linear partial differential equations of second order, which is in particular the basis for Monte Carlo numerical methods for linear PDEs. Since the pioneering work of Peng and Pardoux in the early 1990s, a new type of SDEs called backward stochastic differential equations (BSDEs) has emerged. The two main reasons why this new class of equations is important are the connection between BSDEs and semilinear PDEs, and the fact that BSDEs constitute a natural generalization of the famous Black and Scholes model from Mathematical Finance, and thus offer a natural mathematical framework for the formulation of many new models in Finance.
Download or read book Stochastic Partial Differential Equations written by Étienne Pardoux and published by Springer Nature. This book was released on 2021-10-25 with total page 74 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a concise introduction to the classical theory of stochastic partial differential equations (SPDEs). It begins by describing the classes of equations which are studied later in the book, together with a list of motivating examples of SPDEs which are used in physics, population dynamics, neurophysiology, finance and signal processing. The central part of the book studies SPDEs as infinite-dimensional SDEs, based on the variational approach to PDEs. This extends both the classical Itô formulation and the martingale problem approach due to Stroock and Varadhan. The final chapter considers the solution of a space-time white noise-driven SPDE as a real-valued function of time and (one-dimensional) space. The results of J. Walsh's St Flour notes on the existence, uniqueness and Hölder regularity of the solution are presented. In addition, conditions are given under which the solution remains nonnegative, and the Malliavin calculus is applied. Lastly, reflected SPDEs and their connection with super Brownian motion are considered. At a time when new sophisticated branches of the subject are being developed, this book will be a welcome reference on classical SPDEs for newcomers to the theory.
Download or read book Applied Stochastic Differential Equations written by Simo Särkkä and published by Cambridge University Press. This book was released on 2019-05-02 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: With this hands-on introduction readers will learn what SDEs are all about and how they should use them in practice.
Download or read book Stochastic Differential Equations written by Peter H. Baxendale and published by World Scientific. This book was released on 2007 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first paper in the volume, Stochastic Evolution Equations by N V Krylov and B L Rozovskii, was originally published in Russian in 1979. After more than a quarter-century, this paper remains a standard reference in the field of stochastic partial differential equations (SPDEs) and continues to attract attention of mathematicians of all generations, because, together with a short but thorough introduction to SPDEs, it presents a number of optimal and essentially non-improvable results about solvability for a large class of both linear and non-linear equations.
Download or read book Numerical Solutions of Three Classes of Nonlinear Parabolic Integro Differential Equations written by T Jangveladze and published by Academic Press. This book was released on 2015-11-21 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes three classes of nonlinear partial integro-differential equations. These models arise in electromagnetic diffusion processes and heat flow in materials with memory. Mathematical modeling of these processes is briefly described in the first chapter of the book. Investigations of the described equations include theoretical as well as approximation properties. Qualitative and quantitative properties of solutions of initial-boundary value problems are performed therafter. All statements are given with easy understandable proofs. For approximate solution of problems different varieties of numerical methods are investigated. Comparison analyses of those methods are carried out. For theoretical results the corresponding graphical illustrations are included in the book. At the end of each chapter topical bibliographies are provided. - Investigations of the described equations include theoretical as well as approximation properties - Detailed references enable further independent study - Easily understandable proofs describe real-world processes with mathematical rigor
Download or read book Stochastic Partial Differential Equations Six Perspectives written by René Carmona and published by American Mathematical Soc.. This book was released on 1999 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents the main topics of interest in the field of stochastic partial differential equations (SPDEs), emphasizing breakthroughs and such basic issues as the role of SPDEs in stochastic modeling, how SPDEs arise, and how their theory is applied in different disciplines. Emphasis is placed on the genesis and applications of SPDEs, as well as mathematical theory and numerical methods. Suitable for graduate level students, researchers. Annotation copyrighted by Book News, Inc., Portland, OR
Download or read book Stochastic Partial Differential Equations written by Helge Holden and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Stochastic Partial Differential Equations and Applications written by Giuseppe Da Prato and published by CRC Press. This book was released on 2002-04-05 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on the proceedings of the International Conference on Stochastic Partial Differential Equations and Applications-V held in Trento, Italy, this illuminating reference presents applications in filtering theory, stochastic quantization, quantum probability, and mathematical finance and identifies paths for future research in the field. Stochastic Partial Differential Equations and Applications analyzes recent developments in the study of quantum random fields, control theory, white noise, and fluid dynamics. It presents precise conditions for nontrivial and well-defined scattering, new Gaussian noise terms, models depicting the asymptotic behavior of evolution equations, and solutions to filtering dilemmas in signal processing. With contributions from more than 40 leading experts in the field, Stochastic Partial Differential Equations and Applications is an excellent resource for pure and applied mathematicians; numerical analysts; mathematical physicists; geometers; economists; probabilists; computer scientists; control, electrical, and electronics engineers; and upper-level undergraduate and graduate students in these disciplines.
Download or read book Stochastic Evolution Systems written by Boris L. Rozovsky and published by Springer. This book was released on 2018-10-03 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph, now in a thoroughly revised second edition, develops the theory of stochastic calculus in Hilbert spaces and applies the results to the study of generalized solutions of stochastic parabolic equations. The emphasis lies on second-order stochastic parabolic equations and their connection to random dynamical systems. The authors further explore applications to the theory of optimal non-linear filtering, prediction, and smoothing of partially observed diffusion processes. The new edition now also includes a chapter on chaos expansion for linear stochastic evolution systems. This book will appeal to anyone working in disciplines that require tools from stochastic analysis and PDEs, including pure mathematics, financial mathematics, engineering and physics.
