Review of local martingales and Markov processes of continuous paths. Stochastic integration and stochastic calculus. Brownian motion and partial differential equations. Representations of martingales and change of measure on Wiener space. Weak and strong solutions of stochastic differential equations. Local time for semi-martingales and the theory of Brownian local time. NOTE: This course is open only for graduate students.
3 units · Letter or Credit/No Credit
Review of local martingales and Markov processes of continuous paths. Stochastic integration and stochastic calculus. Brownian motion and partial differential equations. Representations of martingales and change of measure on Wiener space. Weak and strong solutions of stochastic differential equations. Local time for semi-martingales and the theory of Brownian local time. NOTE: This course is open only for graduate students.
Offered in Spring 2027 at Stanford University.