# Stochastic partial differential equations

SDEs taking values in some function space

January 27, 2021 — May 25, 2022

Placeholder, for the multidimensional PDE version of SDEs.

So, how do I handle these?

## 1 Intros that were recommended to me

(Dalang, Khoshnevisan, and Rassoul-Agha 2009a; Dalang and Quer-Sardanyons 2011; Da Prato and Zabczyk 2002, 2014; Holden et al. 1996; Kotelenez 2007; Liu and Röckner 2015; Lord, Powell, and Shardlow 2014)

## 2 As SDEs taking values in a Banach space

Keywords: Q-Wiener process, Cylindrical wiener-process, Banach-space-valued process.

Da Prato and Zabczyk (2014) is the classic reference. A textbook that was recommended to me by Thomas Scheckter was Liu and Röckner (2015), which seems to have same blurb as the older Prévôt and Röckner (2007). There are many free texts, e.g.

Kovács and Larsson Introduction to stochastic partial differential equations, or Michael Scheutzow’s, or Sam Punshon Smith’s.

## 3 Incoming

## 4 References

*The Geometry of Random Fields*.

*Random Fields and Geometry*. Springer Monographs in Mathematics 115.

*Applications of Random Fields and Geometry Draft*.

*Journal of Computational and Graphical Statistics*.

*SIAM Journal on Control*.

*Second Order Partial Differential Equations in Hilbert Spaces*.

*Stochastic Equations in Infinite Dimensions*.

*A Minicourse on Stochastic Partial Differential Equations*. Lecture Notes in Mathematics 1962.

*A minicourse on stochastic partial differential equations*. Lecture notes in mathematics 1962.

*Expositiones Mathematicae*.

*Proceedings of the National Academy of Sciences*.

*Stochastic Differential Equations in Infinite Dimensions: With Applications to Stochastic Partial Differential Equations*. Probability and Its Applications.

*Communications in Mathematical Sciences*.

*The Annals of Applied Probability*.

*Stochastic Partial Differential Equations*.

*WIREs Computational Statistics*.

*Foundations of Modern Probability*. Probability and Its Applications.

*A Minicourse on Stochastic Partial Differential Equations*.

*Stochastic Ordinary and Stochastic Partial Differential Equations: Transition From Microscopic to Macroscopic Equations*.

*Computer Vision: A Reference Guide*.

*Journal of the Royal Statistical Society: Series B (Statistical Methodology)*.

*Stochastic Partial Differential Equations: An Introduction*.

*An Introduction to Computational Stochastic PDEs*. Cambridge Texts in Applied Mathematics.

*Journal of Agricultural, Biological and Environmental Statistics*.

*Stochastic Partial Differential Equations with Lévy Noise: An Evolution Equation Approach*.

*A Concise Course on Stochastic Partial Differential Equations*. Lecture Notes in Mathematics.

*Artificial Neural Networks and Machine Learning – ICANN 2011*. Lecture Notes in Computer Science.

*Journal of Statistical Software*.

*Journal of the Royal Statistical Society: Series B (Statistical Methodology)*.

*Physical Review E*.

*Quarterly Journal of the Royal Meteorological Society*.

*École d’Été de Probabilités de Saint Flour XIV - 1984*.

*Biometrika*.

*Numerical Methods for Stochastic Partial Differential Equations with White Noise*. Applied Mathematical Sciences.