PROBABILITY AND STOCHASTIC PROCESSES - CYCLE 36 - MANDATORY COURSES

All dates: on line via Teams

Prof.ssa Sabrina Mulinacci

Lessons schedule:

Wed    4/11 - 11:00-13:00, 14.00-15.00
Tue   10/11 - 11:00-13:00, 14.00-15.00
Thu   12/11 - 11:00-13:00, 14.00-15.00
Tue   17/11 - 11:00-13:00, 14.00-15.00
Thu   19/11 - 10:00-13:00

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: On line via Teams

Prof. Pietro Rigo

Lessons schedule:

Fri     20/11 - 12:00-14:00
Wed  25/11 - 12:00-14:00
Fri     27/11 - 12:00-14:00
Wed  02/12 - 12:00-14:00
Fri     04/12 -12:00-14:00

Short program:

• Characteristic functions,

• Modes of convergence,

• Laws of large numbers,

• Central limit theorems

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All dates: Seminar Room 1st floor , Department of Statistics, Via Belle Arti 41, Bologna and on line via Teams

Prof. Alberto Lanconelli

Lessons schedule:

Thu   26/11 - 10:00-12:00
Fri     27/11 - 10:00-12:00
Mon  14/12 - 10:00-12:00
Wed  16/12 - 10:00-12:00
Thu    17/12 - 10:00-12:00

Short program:

• Brownian motion: definition, martingale and Markov properties.
• Brownian motion as integrator: failure of Stieltjes integration theory.
• Stochastic differential equations: existence and uniqueness for the strong solution.
• Stochastic differential equations: examples, applications, axiliary results.

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 All dates: On line via Teams

Prof. Silvia Romagnoli

Lessons schedule:

Thu   01/12 - 9:00-12:00
Fri     03/12 - 11:00-13:00
Mon  07/12 - 11:00-13:00
Wed  10/12 - 11:00-14:00

Short program:

• Ito integrals: definition and main properties;
• Ito formula and its applications;
• Change of measure and Girsanov theorem.