Description

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 L vy 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 L vy 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.