Theory and Simulation of Random Phenomena

1 Review of Probability Theory.- 2 Applications to Mathematical Statistics.- 3 Conditional Probability and Conditional Expectation.- 4 Markov Chains.- 5 Sampling of Random Variables and Simulation.- 6 Brownian Motion.- 7 Introduction to Stochastic Calculus and Ito Integral.- 8 Introduction to Stochastic Differential Equations and Applications.- Bibliography.- Solutions. 

Ettore Vitali is a Post-Doctoral Research Associate in the Computational Materials Physics Group, Physics Department, College of William and Mary, Williamsburg, VA, USA. In 2005 he obtained his Master's degree in Physics (summa cum laude) at the Università degli Studi di Milano and in 2008 gained a PhD at the same university for a thesis entitled "Superfluid and supersolid phases of 4He". He has since undertaken postdoctoral fellowships at the Centro di Ricerca e Sviluppo DEMOCRITOS, CNR-INFM, Trieste, Italy and the Università degli Studi di Milano. Dr. Vitali's research interests range across condensed matter physics; probability theory, stochastic processes, stochastic differential equations, and numerical simulation techniques; and statistical methods for ill-posed inverse problems. He is the author of 15 peer-reviewed journal articles. Mario Motta is a Post-Doctoral Research Associate in the Computational Materials Physics Group, Physics Department, College of William and Mary, Williamsburg, VA, USA. He gained Bachelor's and Master's degrees in Physics at the University of Milan in 2010 and 2012 and then completed a PhD in Physics, Astrophysics and Applied Physics from the Università degli Studi di Milano for a thesis entitled "Dynamical properties of many-body systems from Quantum Monte Carlo Simulations", which won the Dr. Davide Colosimo Award for worthy PhD students. His research focuses include topics in condensed matter physics; quantum chemistry; probability theory, stochastic processes, and numerical simulations; and the foundations of quantum mechanics.