# 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. An important special case of functional stochastic DEs.

So, how do I handle these?

## 1 Intros that were recommended to me

(Dalang, Khoshnevisan, and Rassoul-Agha 2009; 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 the 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

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