6 1. PRELUDE
Figure 4. λ = 5
assertion. In other words, the choice of which integration theory or SPDE theory
one uses is mostly a matter of mathematical convenience.
In our case, we find it more convenient to follow the outline of Walsh [138] as
a starting point mainly because that approach lends itself particularly well to the
analysis of the sample functions of the solution, and properties such as intermittency
are deeply connected to that analysis.
Ordinarily one might wish to close the prologue with a brief description of the
literature on the topic of discussion, here that is SPDEs. I have found it a particu-
larly difficult task to write this portion, mainly because stochastic partial differential
equations have been developed independently and at more or less similar times by
various research groups and individuals for a variety of different scientific reasons.
Attempts at careful documentation of the history of the subject are complicated
further by the fact that much of the literature on applied SPDEs lies outside of the
traditional mathematics literature. Therefore, let me just mention, in passing, a
relatively-short bibliography on SPDEs that is more directly related to the topics
of this course.
Some of the earlier papers on SPDEs can be found in the works of Baklan
[5, 6], Baklan and
ˇ
Sataˇ svili [7], Belopol skaja and Dalec ki˘ ı [9], Bensoussan and
Temam [11], Chow [18], Curtain and Falb [28, 29], Daletski˘ ı and Fomin [37, 39],
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