Prof. Pietro Rigo

Argomenti del programma: Probability spaces and their elementary properties Various definitions of probability (just a hint) Random variables and their distributions Independence Probability measures on R and R^n (including distribution functions, and, in case of R, discrete, singular continuous, and absolutely continuous probability laws) List of the main probability measures on R and normal distribution on R^n Transform of random…

Argomenti del programma: Brief review of a few basic concepts on probability theory Conditional expectation General notions about stochastic processes: Definition, paths, filtrations, stopping times, finite dimensional distributions Existence of processes with given finite dimensional distributions Martingales Markov chains Stationary and exchangeable sequences Random walks Brownian motion Poisson process Levy and r enewal processes

Argomenti del programma: Probability spaces A few elementary notions of measure theory Random variables and their probability distributions Probability measures on R and R^n Moments Conditional distributions and conditional expectations Characteristic functions Weak convergence of probability measures Other modes of convergence Borel-Cantelli Lemma Laws of large numbers Central limit theorems Infintely divisible and stable distributions