Stochastic partial differential equations

SDEs taking values in some function space

January 27, 2021 — May 25, 2022

Banach space
dynamical systems
Hilbert space
Lévy processes
probability
SDEs
signal processing
spatial
stochastic processes
time series

Placeholder, for the multidimensional PDE version of SDEs. An important special case of functional stochastic DEs.

Figure 1: This picture of ice floes on the Bering shelf looks like it might be some kinda stochastic PDE thing, right? No further metadata because Internet archive took their content off Flickr, sorry.

So, how do I handle these?

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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