Elements of Probability and Statistics

Massimo Campanino was born on 1952. On 1975 he got the degree on Mathematics at the University of Rome, Italy, under the supervisorship in Mathematics under the supervisorship of prof. Bruno de Finetti. Since 1990 he is full Professor of Probability at the University of Bologna, Italy. He has been visitor at I. H. E. S. of Bures-sur-Yvette (France), at the University of Princeton and at the University of California Irvine. He has performed research on random fields, dynamical systems random processes, systems with random potential and in random environment, percolation. He is the author of works in collaboration with H. Epstein and D. Ruelle where the existence of a solution of Feigenbaum’s functional equation, related to the universal behaviour of one-dimensional dynamical systems, was first proved. In works in collaboration with D. Ioffe he proved the Ornstein-Zernike behaviour for Bernoulli percolation below the critical probability and then with D. Ioffe and Y. Velenik for finite range Ising models. He has been national coordinator of the 2006 Prin project "Percolation, random fields, evolution of stochastic interacting systems" and of the 2009 Prin project "Random fields, percolation and stochastic.Francesca Biagini was born in 1973. In Pisa she got the degree in Mathematics at the University in 1996 and attended the Scuola Normale, where she also obtained her PhD in Mathematics with specialization in Financial Mathematics in 2001. In 1999 she got a position as ricercatore at the University of Bologna. She moved then in 2005 to the University of Munich as associate professor. In 2009 she got the Chair of Financial and Insurance Mathematics at the University of Munich. She has been visiting at the University of Oslo, Evry, Toulose, Singapore, UCSB, Columbia University and Stockholm School of Economics. Her field of research concerns mainly martingale methods for financial and insurance markets and stochastic calculus for fractional Brownian motion.She is presently Member of the Council of the Bachelier Finance Society and associate editor for the journal Stochastic Analysis and Applications.

"The authors are to be commended for their attempt to show that de Finetti's approach can in fact be used successfully in introducing and developing probability theory." (A. I. Dale, Mathematical Reviews, November, 2016)

• 1 Random numbers.- 2 Discrete distributions.- 3 One-dimensional absolutely continuous distributions.- 4 Multi-dimensional absolutely continuous distributions.- 5 Convergence of distributions.- 6 Discrete time Markov chains.- 7 Continuous time Markov chains.- 8 Statistics.- 9 Combinatorics.- 10 Discrete distributions.- 11 One-dimensional absolutely continuous distributions.- 12 Absolutely continuous and multivariate distributions.- 13 Markov chains.- 14 Statistics.- 15 Elements of combinatorics.- 16 Relations between discrete and absolutely continuous distributions.- 17 Some discrete distributions.- 18 Some one-dimensional absolutely continuous distributions.- 19 The normal distribution.- 20 Stirling's formula.- 21 Elements of analysis.- 22 Bidimensional integrals.