These notes are based on a postgraduate course I gave on stochastic dif-
ferential equations at Edinburgh University in the spring 1982. No previous
knowledge about the subject was assumed, but the presentation is based on
some background in measure theory.
There are several reasons why one should learn more about stochastic
di®erential equations: They have a wide range of applications outside mathe-
matics, there are many fruitful connections to other mathematical disciplines
and the subject has a rapidly developing life of its own as a fascinating re-
search ¯eld with many interesting unanswered questions.
Unfortunately most of the literature about stochastic di®erential equa-
tions seems to place so much emphasis on rigor and completeness that it
scares many nonexperts away. These notes are an attempt to approach the
subject from the nonexpert point of view: Not knowing anything (except ru-
mours, maybe) about a subject to start with, what would I like to know ¯rst
of all? My answer would be: