Probability Theory II

Andrea Pascucci is a professor of Probability and Mathematical Statistics at the Alma Mater Studiorum - University of Bologna. His research activity encompasses various aspects of the theory of stochastic differential equations for diffusions and jump processes, degenerate partial differential equations, and their applications to mathematical finance. He has authored 6 books and over 80 scientific articles on the following topics: linear and nonlinear Kolmogorov-Fokker-Planck equations; regularity and asymptotic estimates of transition densities for multidimensional diffusions and jump processes; free boundary problems, optimal stopping, and applications to American-style financial derivatives; Asian options and volatility models. He has been invited as a speaker at more than 40 international conferences. He serves as an editor for the Journal of Computational Finance and is the director of a postgraduate program in Mathematical Finance at the University of Bologna.

1 Stochastic processes.- 2 Markov processes.- 3 Continuous processes.- 4 Brownian motion.- 5 Poisson process.- 6 Stopping times.- 7 Strong Markov property.- 8 Continuous martingales.- 9 Theory of variation.- 10 Stochastic integral.-  11 Itô's formula.- 12 Multidimensional stochastic calculus.- 13 Change of measure and martingale representation.- 14 Stochastic differential equations.- 15 Feynman-Kac formulas.- 16 Linear stochastic equations.- 17 Strong solutions.- 18 Weak solutions.- 19 Complements.-20 A primer on parabolic PDEs.