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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.

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Good papers on stochastic differential equations with applications in finance

For basic theory: Stephen Shreve's books (Stochastic Calculus for Finance I and II) and Martingale Methods in Financial Modelling by Marek Musiela and Marek Rutkowski. Also have a look at Oksendal's b …
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