We examine generalizations of random variables and martingales. We prove a new convergence theorem for setvalued martingales. We also generalize a well known characterization of se...
We present a new technique for constructing and analyzing couplings to bound the convergence rate of finite Markov chains. Our main theorem is a generalization of the path couplin...
This is a great draft book about stochastic calculus and finance. It covers large number of topics such as Introduction to Probability Theory, Conditional Expectation, Arbitrage Pr...
We give a simple combinatorial proof of the Chernoff-Hoeffding concentration bound [Che52, Hoe63], which says that the sum of independent {0, 1}-valued random variables is highly ...
New families of Fisher information and entropy power inequalities for sums of independent random variables are presented. These inequalities relate the information in the sum of n ...