This book covers basic theory as well as computational and analytical techniques to solve physical, biological, and financial problems. This second edition incorporates new material concerning stochastic PDEs driven by Levy-type noise. It includes new sections on stochastic differential equations of Levy type as well as stochastic parabolic, hyperbolic, and evolution equations with Poisson noise. This edition also provides new applications of stochastic PDEs to population biology and finance and an updated section on parabolic equations and related elliptic problems in Gauss-Sobolev spaces.

Preliminaries. Scalar Equations of First Order. Stochastic Parabolic Equations. Stochastic Parabolic Equations in the Whole Space. Stochastic Hyperbolic Equations. Stochastic Evolution Equations in Hilbert Spaces. Asymptotic Behavior of Solutions. Further Applications. Diffusion Equations in Infinite Dimensions. Bibliography. Index.