Introduction to SPDEs from Probability and PDE

Abstract

Lecture notes accompanying an 8hr hour mini-course on SPDE given at Boğaziçi University, Istanbul in June/July 2025. They are based on earlier notes of a shorter mini-course given at the University of Oxford in 2021. The main focus of these notes is on an exposition of the variational method for monotone and coercive SPDE. A recap of the necessary functional analysis, operator theory and stochastic analysis on Hilbert spaces is included, with additional references. The final chapter contains a discussion of the pathwise approach.

Examples updated in Chapters 2 and 3; Acknowledgments added; 90 pages