I’m interested to know whether PDEs, and both analytical and numerical methods to solve them, have much significance in probability theory and stochastic processes? I am aware that financial mathematics is very much based on stochastic calculus, and I think I read somewhere that solving some of these equations in finance can be reduced down to solving the heat equation (correct me if I’m wrong)? I’d just be interested to know if PDEs and methods to solve them do/can play an important role in topics in probability, and if so what these topics are (other than finance)? Thank you.
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maths54321
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Google Feynman Kac theorem. – Jun 24 '20 at 19:18
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... or for Kolmogorov equation (see also this, for a start) – saz Jun 25 '20 at 06:21