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A Minicourse on Stochastic Partial Differential Equations

2009 Mathematics
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Release : 2009
Genre : Mathematics
Kind : eBook
Book Rating : 934/5 ( reviews)

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Book Synopsis A Minicourse on Stochastic Partial Differential Equations by : Robert C. Dalang

Download or read book A Minicourse on Stochastic Partial Differential Equations written by Robert C. Dalang. This book was released on 2009. 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.

Stochastic Partial Differential Equations, Second Edition

2014-12-10 Mathematics
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Release : 2014-12-10
Genre : Mathematics
Kind : eBook
Book Rating : 552/5 ( reviews)

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Book Synopsis Stochastic Partial Differential Equations, Second Edition by : Pao-Liu Chow

Download or read book Stochastic Partial Differential Equations, Second Edition written by Pao-Liu Chow. This book was released on 2014-12-10. 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.

A Concise Course on Stochastic Partial Differential Equations

2007-06-08 Mathematics
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Release : 2007-06-08
Genre : Mathematics
Kind : eBook
Book Rating : 808/5 ( reviews)

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Book Synopsis A Concise Course on Stochastic Partial Differential Equations by : Claudia Prévôt

Download or read book A Concise Course on Stochastic Partial Differential Equations written by Claudia Prévôt. This book was released on 2007-06-08. 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.

Stochastic Partial Differential Equations

2013-12-01 Mathematics
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Release : 2013-12-01
Genre : Mathematics
Kind : eBook
Book Rating : 152/5 ( reviews)

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Book Synopsis Stochastic Partial Differential Equations by : Helge Holden

Download or read book Stochastic Partial Differential Equations written by Helge Holden. This book was released on 2013-12-01. 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.

Stochastic Partial Differential Equations With Additive Gaussian Noise - Analysis And Inference

2022-10-11 Mathematics
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Release : 2022-10-11
Genre : Mathematics
Kind : eBook
Book Rating : 473/5 ( reviews)

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Book Synopsis Stochastic Partial Differential Equations With Additive Gaussian Noise - Analysis And Inference by : Ciprian A Tudor

Download or read book Stochastic Partial Differential Equations With Additive Gaussian Noise - Analysis And Inference written by Ciprian A Tudor. This book was released on 2022-10-11. Available in PDF, EPUB and Kindle. Book excerpt: The stochastic partial differential equations (SPDEs) arise in many applications of the probability theory. This monograph will focus on two particular (and probably the most known) equations: the stochastic heat equation and the stochastic wave equation.The focus is on the relationship between the solutions to the SPDEs and the fractional Brownian motion (and related processes). An important point of the analysis is the study of the asymptotic behavior of the p-variations of the solutions to the heat or wave equations driven by space-time Gaussian noise or by a Gaussian noise with a non-trivial correlation in space.The book is addressed to public with a reasonable background in probability theory. The idea is to keep it self-contained and avoid using of complex techniques. We also chose to insist on the basic properties of the random noise and to detail the construction of the Wiener integration with respect to them. The intention is to present the proofs complete and detailed.

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