Introduction to SPDEs from Probability and PDE
Probability
2025-08-01 v3 Analysis of PDEs
Abstract
Lecture notes accompanying an 8hr hour mini-course on SPDE given at Bo\u{g}azi\c{c}i 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.
Keywords
Cite
@article{arxiv.2111.13160,
title = {Introduction to SPDEs from Probability and PDE},
author = {Avi Mayorcas},
journal= {arXiv preprint arXiv:2111.13160},
year = {2025}
}
Comments
Examples updated in Chapters 2 and 3; Acknowledgments added; 90 pages