Stochastic Processes

Construction of Brownian motion, convergence in C[0, 8), D[0, 8), Donsker's invariance principle,
properties of the Brownian motion, continuous-time martingales, optional sampling theorem,
Doob-Meyer decomposition, stochastic integration, Ito's formula, martingale representation theorem,
Girsanov's theorem, Brownian motion and the heat equation, Feynman-Kac formula, diffusion processes
and stochastic differential equations, strong and weak solutions, martingale problems.

Books

• Billingsley, P., Convergence of Probability Measures, Wiley-interscience, 1999.
• Karatzas, I. and Shreve, S., Brownian Motion and Stochastic Calculus, Springer, 2006.
• Revuz, D. and Yor, M., Continuous Martingales and Brownian motion, Springer, 2006.
• Oksendal, B., Introduction to Stochastic Differential Equations, Springer, 2007.