Probability and stochastic processes (2022)

proff. S. Mulinacci, P. Rigo

  • Date:

    04 NOVEMBER
    -
    21 DECEMBER 2021
     from 10:00 to 16:00

  • Event location: Aula IV, Via Belle Arti 41 and STAT PhD Classes Virtual Room

  • Type: Cycle 37 - Mandatory Courses

Teachers: Sabrina Mulinacci and Pietro Rigo
Length: 38 hours

 

The main goal of this course is to provide some basic knowledge on Probability
Theory and Stochastic Processes. The level of the course strongly depends on the
students' skills on such topics. Special attention is paid to those arguments which
are commonly used in statistical inference, such as conditioning and asymptotics.
The exam is oral and consists of an interview with the teachers. However, the
student may be required to discuss (not necessarily to solve) some simple exercises.
The latter are obvious versions of the exercises developed by the teachers during
the course.

Among other things, the following topics will be covered:

  • Probability spaces;
  • Independence;
  • Measurability and random variables;
  • Probability measures on (the Borel sets of) R and Rn;
  • Moments;
  • Conditional expectation and conditional probability;
  • Characteristic functions;
  • Stochastic convergence;
  • Some basic theory of stochastic processes (paths, filtrations, finite dimensional distributions);
  • Martingales;
  • Brownian motion;
  • Some elementary Ito theory (subjected to the available time).

References

P. Billingsley "Probability and Measure", John Wiley

 

Schedule

  • Prof. S.Mulinacci: 

    4/11 10.00-13.00
    10/11 10.30-12.30 and 13.30 - 14.30
    11/11 14.30-16.30
    16/11 14.30-16.30
    17/11 10.30-12.30 and 13.30 - 14.30
    23/11 14.30-16.30
    24/11 10.30-12.30 and 13.30 - 14.30
    25/11 14.30-16.30
    17/12 10.30-13.30

  • Prof. P.Rigo:
    29/11 13-15
    30/11 11-13
    2/12 12-14
    7/12 11-13
    10/12 14-16
    13/12 13-15
    17/12 14-16
    20/12 14-16
    21/12 14-16