PROBABILITY AND STOCHASTIC PROCESSES - CYCLE 35 - MANDATORY COURSES

All dates: Seminar Room 1st floor, Department of Statistics, Via Belle Arti 41, Bologna

Prof.ssa Sabrina Mulinacci

Lessons schedule:

Tue     5/11 - 14:00-16:00
Thu     8/11 - 15:00-17:00
Tue   12/11 - 15:00-17:00
Thu   14/11 - 10:00-12:00
Tue   19/11 - 14:00-16:00
Thu   21/11 -  10:00-12:00
Tue     3/12 -  14:00-17:00

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

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All dates: Seminar Room 1st floor, Department of Statistics, Via Belle Arti 41, Bologna

Prof Alberto Lanconelli

Lessons schedule:

Tue    26/11 - 14:00-16:00

Wed  27 /11 - 11:00-13:00
Thu    28/11 - 14:00-16:00

Wed   04/12 - 11:00-13:00
Thu    05/12 - 11:00-13:00

Mon 09/12  - 14:00-16:00

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

Prof.ssa Silvia Romagnoli

Lessons schedule:

Tue   7/1 11-14
Wed  8/1 11-14
Thu   9/1 11-14
Fri   10/1 11-14

Short program:

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