Random Series and Stochastic Integrals: Single and Multiple (Probability and Its Applications)

This volume studies the foundations of the theory of linear and nonlinear forms in single and multiple random variables including single and multiple random series and stochastic integrals, both Gaussian and non-Gaussian. Its topic is intimately connected with a number of classical problems of probability theory such as the summation of independent random variables, martingale theory and the Weiner theory of polynomial chaos, as well as with several application areas such as stochastic analysis, limit theorems for symmetric statistics, representation of random fields, partial differential equations and quantum field theory. The emphasis is on domination principles for comparison of sequences of random variables and on decoupling techniques. The volume is intended for researchers and graduate students in probability theory, stochastic processes, theoretical statistics and in several areas of theoretical physics and engineering.