The study of chaos expansions and multiple Wiener-Ito integrals has become a field of considerable interest in applied and theoretical areas of probability, stochastic processes, mathematical physics, and statistics. Divided into four parts, this book features a wide selection of surveys and recent developments on these subjects. Part 1 introduces the concepts, techniques, and applications of multiple Wiener-Ito and related integrals. The second part includes papers on chaos random variables appearing in many limiting theorems. Part 3 is devoted to mixing, zero-one laws, and path continuity properties of chaos processes. The final part presents several applications to stochastic analysis.
Table of Contents
Multiple Wiener-Ito Integrals: An Introductory Review, C. Houdre, V. Perez-Abreu, and A.S. Ustunel.
The Hu-Meyer Formula: A View of the Problem with Special Attention to the Poisson Case, J.L. Sole and F. Utzet.
Remarks on the Existence of k-Traces, G.W. Johnson and G. Kallianpur.
Multiple Wiener-Ito Integrals and a Multivariate Version of Schoenberg's Theorem, O. Kallenberg.
The State of Decoupling: A Survey, J. Szulga.
MWI Expansions for Functionals Related to Level-Crossing Counts, E.V. Slud.
Scaling Limits of Solutions of Burgers' Equation with Singular Gaussian Initial Data, D. Surgailis and W.A. Woyczynski.
Weak Convergence in Dynamical Systems to Self-Similar Processes with Time Average Representation, M.T. Lacey.
On Exact Tails for Limiting Distributions of U-Statistics in the Second Gaussian Chaos, P. Imkeller.
Limit Theorems for Empirical Processes under Dependence, M.A. Arcones and B. Yu.
Mixing for Multiple Wiener-Ito Integral Processes, D.W. Chambers.
Zero-One Laws for Multiple Stochastic Integrals, J. Rosinski and G. Samorodnitsky.
Continuity of Some Gaussian Chaoses, M.B. Marcus.
Some Formulas for Anticipative Girsanov Transformations, J.A. Leon and P. Protter.
Absolute Continuity of Processes and a Derivation Rule, M.E. Caballero and B. Fernandez.
Smoothness of Local Time and Related Wiener Functionals, D. Nualart and J. Vives.
Distributions on Wiener Space and Fluctuation Limits of Poisson Systems of Brownian Bridges, L.G. Gorostiza.
Ito-Ramer, Skorohod and Ogawa Integrals with Respect to Gaussian Processes and Their Interrelationship, L. Gawarecki and V. Mandrekar.