Proof-based approach to stochastic processes. Brownian motion. Continuous martingales. Stochastic integration. Ito formula. Girsanov's Theorem. Stochastic differential equations. Feynman-Kac formula. Markov Processes. Local times. Levy processes. Semimartingales and the general stochastic integral. Stable processes. Fractional Brownian motion.

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