Brownian Motion, Martingales, and Stochastic Calculus
by Jean-François Le Gall · Springer
Rigorous graduate text (Springer GTM 274) on continuous-time stochastic calculus. Covers Gaussian processes, Brownian motion, continuous semimartingales, stochastic integration, Girsanov, Markov processes, SDEs and their links to PDEs, and local times. Endpoint for readers who want the full measure-theoretic theory. It is shorter and more modern than Karatzas & Shreve and is the assigned text at MIT's graduate stochastic calculus course.
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