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Stochastic Partial Differential Equations: A Comprehensive Guide for Students and Researchers

Colin Foster

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Published in Stochastic Partial Differential Equations (Universitext)

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Stochastic partial differential equations (SPDEs) are a powerful tool for modeling complex phenomena in a wide range of fields, including physics, biology, and finance. SPDEs are used to model everything from the evolution of fluid flow to the spread of epidemics. This book provides a comprehensive to SPDEs, with a focus on mathematical foundations and numerical methods.

Stochastic Partial Differential Equations (Universitext)

by Teri Woods

4 out of 5

Language	:	English
File size	:	9034 KB
Screen Reader	:	Supported
Print length	:	522 pages

What are SPDEs?

SPDEs are partial differential equations that contain random elements. This means that the solution to an SPDE is not a deterministic function, but rather a random variable. SPDEs are often used to model phenomena that are inherently stochastic, such as the evolution of fluid flow or the spread of epidemics.

Mathematical foundations of SPDEs

The book begins with a review of the mathematical foundations of SPDEs. This includes a discussion of the theory of probability, measure theory, and functional analysis. The book also provides an to the theory of stochastic processes, which is essential for understanding SPDEs.

Numerical methods for SPDEs

The second part of the book focuses on numerical methods for SPDEs. This includes a discussion of finite difference methods, finite element methods, and Monte Carlo methods. The book also provides an to the theory of adaptive mesh refinement, which is essential for solving SPDEs efficiently.

Applications of SPDEs

The third part of the book provides an overview of applications of SPDEs. This includes a discussion of applications in physics, biology, and finance. The book also provides an to the theory of stochastic control, which is essential for applications of SPDEs in engineering and finance.

This book is a comprehensive to SPDEs, with a focus on mathematical foundations and numerical methods. The book is written in a clear and accessible style, making it suitable for both students and researchers new to the field.