Enrolment options
Course objectives
The course aims to put the student in a position to understand the mathematical formulation of various models of applied sciences and financial mathematics which involve stochastic differential equations. The course uses probabilistic concepts and tools that are developed in the course ``Probability Theory'' and elements of Functional Analysis (see ``Analysis''); these concepts are briefly mentioned in the first lectures. The proofs of the main results of the course are carried out completely. They show important links between Analysis and Probability. To improve the skills of reading and study the teacher proposes the reading of some scientific articles. Together with the course ``Stochastic Processes'' it suggests an approach to the research in stochastic environments. The course also provides basic concepts on parabolic equations of Kolmogorov type.
A module of the course, included in the overall courseload, will be taught by visiting professor Francesco Russo (ENSTA ParisTech, France) on "BM and stochastic integrals" (cf. International visiting professorsopen_in_newopen_in_newopen_in_new).