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Stochastic ordinary and partial differential equations generalize the concepts of ordinary and partial differential equations to the setting where the unknown is a stochastic process.
5
votes
Accepted
Reference for Feynman-Kac
Please see p.282 of the following ref, it does not call it Feynman-Kac Formula but the whole section 5 is discussing it. It formalized the diffusion using a tensor field over a manifold which is the m …
2
votes
Accepted
Any modern/recent version of Ito & McKean?
Again I had to point out my favorite book on diffusion process below. The authors belong to Ito school, so their understanding is quite insightful and consistent with Ito's. The understanding of his s …
7
votes
Does a theory of stochastic differential algebras exist?
Yes. A systematic study of stochastic (differential) algebra could be found in
Grenander, Ulf. Probabilities on algebraic structures. Dover Books, 1981.
Grenander studied the operation of integ …