A Concise Course on Stochastic Partial Differential Equations

A concise course on stochastic partial differential equations provides a solid introduction to the analysis of (nonlinear) stochastic partial differential equations (SPDE) of the evolutionary type. These lectures focus on modeling dynamic systems that are influenced by both natural and human-made factors. The emphasis is on the use of stochastic integrals in conjunction with a cylindrical Wiener process, with results easily extendable to more general types of noise. The lectures are structured to minimize technical details while offering a comprehensive introduction to variational approaches for analyzing SPDE. Important background information, including definitions and results from the theory of Hilbert spaces, is included in the appendices to enable readers to develop an independent understanding.