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Stochastic Partial Differential Equations (SPDEs) have received much attention in recent years, culminating in the fields medal of Martin Hairer.

A rigorous mathematical starting point for the studies of SPDEs is often quoted to be the Saint-Flour lecture notes of John B. Walsh titled "An introduction to stochastic partial differential equations" in which Walsh describes the random field approach for studying SPDEs, that is one makes sense of SPDEs as "multidimensional" SDEs (rather than making sense of SPDEs as an infinite-dimensional system of SDEs). So who was this man whom many crucial ideas date back to?

There is one man matching this name, namely John Bradstreet Walsh who did his PhD at the University of Illinois at Urbana-Champaign in 1966 under the supervision of Joseph Leo Doob titled "Probability and a Dirichlet Problem for Multiply Superharmonic Functions", however I can not find any information on this mathematician. If this is the right person is there any information on him and if not who was Walsh?

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Yes, that is the one.
More information HERE
(If your library subscribes to MathSciNet, and you go to that page from your library, then you will be able to get links to Walsh's 70 or so publications, reviews, etc.)
In particular, we can find that the lectures you mention are published as:

Walsh, John B. "An introduction to stochastic partial differential equations". École d'été de probabilités de Saint-Flour, XIV—1984, 265–439, Lecture Notes in Math., 1180, Springer, Berlin, 1986.

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