January  2021, 41(1): 471-487. doi: 10.3934/dcds.2020264

A brief and personal history of stochastic partial differential equations

Laboratoire de Probabilités, Statistique et Modélisation, Sorbonne Université, Université de Paris, CNRS, 4, Place Jussieu, 75005 Paris, France

Received  December 2019 Published  July 2020

Fund Project: The author is supported by the grant ANR-15-CE40-0020 - LSD - Large Stochastic Dynamical Models in Non-Equilibrium Statistical Physics (2015)

We trace the evolution of the theory of stochastic partial differential equations from the foundation to its development, until the recent solution of long-standing problems on well-posedness of the KPZ equation and the stochastic quantization in dimension three.

Citation: Lorenzo Zambotti. A brief and personal history of stochastic partial differential equations. Discrete & Continuous Dynamical Systems, 2021, 41 (1) : 471-487. doi: 10.3934/dcds.2020264
References:
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show all references

References:
[1]

S. Albeverio and S. Kusuoka, The invariant measure and the flow associated to the $\Phi^4_3$-quantum field model, preprint, 2017, arXiv: 1711.07108. Google Scholar

[2]

S. Albeverio and R. Høegh-Krohn, Dirichlet forms and diffusion processes on rigged Hilbert spaces, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 40 (1977), 1-57.  doi: 10.1007/BF00535706.  Google Scholar

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A. Bensoussan and R. Temam, Équations aux dérivées partielles stochastiques non linéaires. I, Israel J. Math., 11 (1972), 95-129.  doi: 10.1007/BF02761449.  Google Scholar

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[12]

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[14]

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[17]

K.-T. Chen, Integration of paths, geometric invariants and a generalized Baker-Hausdorff formula, Ann. of Math. (2), 65 (1957), 163-178.  doi: 10.2307/1969671.  Google Scholar

[18]

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[19]

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I. Corwin, Kardar-Parisi-Zhang universality, Notices Amer. Math. Soc., 63 (2016), 230-239.  doi: 10.1090/noti1334.  Google Scholar

[21]

G. Da Prato and J. Zabczyk, Ergodicity for Infinite-Dimensional Systems, London Mathematical Society Lecture Note Series, vol. 229, Cambridge University Press, Cambridge, 1996. doi: 10.1017/CBO9780511662829.  Google Scholar

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[23]

G. Da Prato, M. Iannelli and L. Tubaro, Stochastic differential equations in Banach spaces, variational formulation, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Nat. (8), 61 (1976), 168–176 (1977).  Google Scholar

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