Examination procedure
<p>oral exam</p>
Examination procedure notes
<p>Oral exam, possibly focused on a specific advanced topic</p>
Prerequisites
The course is tuned for the PhD program in Computation and Finance but proved to be of interest, in previous editions, also for students in Math and Physics of Master level.
Syllabus
1) General introductory elements of probabilty, Markov chains, stochastic processes and Brownian motion
(this part is supposed to be partially known ad will be explained in a form of summary, possibly with insights depending on the audience)
2) Continuous time Markov chains and stochastic differential equations: definitions, infinitesimal generators and rules of calculus, examples
(this part is not supposed to be known, but will nevethless be explained in concise form, without many proofs)
3) Interacting particle systems, deterministic and stochastic
(this part will be very detailed, used to show the practical implementation of the general notions described above in a complex theoretical setting).
Bibliographical references
notes of the teacher