Theory of stochastic calculus

The lecture this week is from 8:15 to 11:00.

Topics: The stochastic integral for simple predictable processes and its properties. The stochastic integral as a continuous martingale. Extension of the stochastic integral to the space of mean-square integrable and predictable processes via the Itô isometry.  Extending the stochastic integral via localization, local martingales, Itô's formula, quadratic variation of a martingale, towards integration with respect to continuous martingales.