PROBABILITY AND STOCHASTIC PROCESSES - CYCLE 34 - MANDATORY COURSES

  • Date:

    06 NOVEMBER
    -
    19 DECEMBER 2018
     

  • Type: Cycle 34 - Mandatory Courses

All dates: Department of Statistics, Via Belle Arti 41, Bologna

Prof.ssa Sabrina Mulinacci

Lessons schedule:

Wed   6/11 - 10:00-12:00 a.m - Seminar Room 1st floor
Fri      8/11 - 10:00-12:00 a.m - Seminar Room 1st floor
Wed 13/11 - 10:00-12:00 a.m - Seminar Room 1st floor
Fri    15/11 - 10:00-12:00 a.m - Seminar Room 1st floor
Wed 20/11 - 10:00-12:00 a.m - Seminar Room 1st floor
Fri    22/11 -  09:00-12:00 a.m - Seminar Room 1st floor

Short program:

  • Probability spaces
  • Independence: Borel-Cantelli lemmas and Kolmogorov Zero-One law
  • Random Variables:  convergence of sequences of random variables
  • Conditional Expectation
  • Stochastic processes in discrete times: martingales

 


Prof Alberto Lanconelli

Lessons schedule:

Tue 26/11 -  11:00-13:00 a.m - Seminar Room 1st floor
Thu 28/11 -  11:00-13:00 a.m - Seminar Room 1st floor
Fri   29/11 -  11:00-13:00 a.m - Seminar Room 1st floor
Tue 03/12 -  11:00-13:00 a.m - Room IV 2nd floor
Thu 05/12 -  14:00-16:00 p.m - Room IV 2nd floor
Fri   06/12 -  11:00-13:00 a.m - Seminar Room 1st floor

Short program:

  • Characteristic function of a random variable
  • Convergence in distribution
  • Law of large numbers and central limit theorem
  • Brownian motion: definition and existence
  • Brownian motion: martingale and path properties



Lessons schedule:

Tue  11/12 -  09:00-12:00 a.m, Seminar Room 1st floor
Wed 12/12 - 10:00-13:00 a.m, Seminar Room 1st floor
Thu  13/12 -  09:00-12:00 a.m, Seminar Room 1st floor
Thu  19/12 -  10:00-13:00 a.m, Seminar Room 1st floor

Short program:

  • Stopping times and martingales (discrete and continuous times)
  • Stochastic integral
  • Stochastic differential calculus
  • Chance of measure 
  • Kolmogorov PDE