Placeholder, for the multidimensional PDE version of SDEs.

[This

So, how do I handle these?

## 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)

## 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.

## References

*The Geometry of Random Fields*. SIAM ed. Philadelphia: Society for Industrial and Applied Mathematics.

*Random Fields and Geometry*. Springer Monographs in Mathematics 115. New York: Springer.

*Applications of Random Fields and Geometry Draft*.

*Journal of Computational and Graphical Statistics*29 (2): 274–85.

*SIAM Journal on Control*13 (1): 89–104.

*Second Order Partial Differential Equations in Hilbert Spaces*. Cambridge, UK; New York: Cambridge University Press.

*Stochastic Equations in Infinite Dimensions*. Cambridge University Press.

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

*A minicourse on stochastic partial differential equations*. Vol. 1962. Lecture notes in mathematics 1962. Berlin: Springer.

*Expositiones Mathematicae*29 (1): 67–109.

*Stochastic Differential Equations in Infinite Dimensions: With Applications to Stochastic Partial Differential Equations*. Probability and Its Applications. Berlin Heidelberg: Springer-Verlag.

*The Annals of Applied Probability*17 (5-6): 1657–1706.

*Communications in Mathematical Sciences*3 (4): 587–603.

*Stochastic Partial Differential Equations*. Boston, MA: Birkhäuser Boston.

*WIREs Computational Statistics*8 (2): 112–25.

*Foundations of Modern Probability*. 2nd ed. Probability and Its Applications. New York: Springer-Verlag.

*A Minicourse on Stochastic Partial Differential Equations*, edited by Davar Khoshnevisan and Firas Rassoul-Agha, 1962:1–38. Berlin, Heidelberg: Springer Berlin Heidelberg.

*Stochastic Ordinary and Stochastic Partial Differential Equations: Transition From Microscopic to Macroscopic Equations*. Springer Science & Business Media.

*Computer Vision: A Reference Guide*, edited by Katsushi Ikeuchi, 770–75. Boston, MA: Springer US.

*Journal of the Royal Statistical Society: Series B (Statistical Methodology)*73 (4): 423–98.

*Stochastic Partial Differential Equations: An Introduction*. Springer.

*An Introduction to Computational Stochastic PDEs*. 1st edition. Cambridge Texts in Applied Mathematics. New York, NY, USA: Cambridge University Press.

*Journal of Agricultural, Biological and Environmental Statistics*25 (1): 1–16.

*Stochastic Partial Differential Equations with Lévy Noise: An Evolution Equation Approach*. 1 edition. Cambridge ; New York: Cambridge University Press.

*A Concise Course on Stochastic Partial Differential Equations*. Lecture Notes in Mathematics. Berlin Heidelberg: Springer-Verlag.

*Artificial Neural Networks and Machine Learning – ICANN 2011*, edited by Timo Honkela, Włodzisław Duch, Mark Girolami, and Samuel Kaski, 6792:151–58. Lecture Notes in Computer Science. Berlin, Heidelberg: Springer.

*Journal of Statistical Software*63 (14).

*Journal of the Royal Statistical Society: Series B (Statistical Methodology)*77 (1): 3–33.

*Physical Review E*88 (5): 052909.

*Quarterly Journal of the Royal Meteorological Society*145 (722): 2255–71.

*École d’Été de Probabilités de Saint Flour XIV - 1984*, edited by P. L. Hennequin, 1180:265–439. Springer Berlin Heidelberg.

*Biometrika*41 (3/4): 434–49.

*Numerical Methods for Stochastic Partial Differential Equations with White Noise*. Vol. 196. Applied Mathematical Sciences. Cham: Springer International Publishing.

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