Stochastic Differential Equations: An Introduction with Applications (6th ed.)
by Bernt Øksendal · Springer (Universitext)
Classic graduate introduction to Itô calculus and SDEs. Chapters cover the Itô integral, Itô formula, martingale representation, diffusions, Girsanov's theorem, filtering (Kalman-Bucy), optimal stopping, stochastic control and mathematical finance. The sixth edition adds solutions to many exercises. It covers the filtering application, which Shreve does not. It is the standard second book after Shreve or Evans.
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