Stochastic Processes

On behalf of those of us who in various ways have con tributed to this volume, and on behalf of all of his colleagues, students and friends throughout the world-wide scientific com munity, we dedicate this volume to Gopinath Kallianpur as a tribute to his work and in appreciation for the insights which he has so graciously and generously offered, and continues to offer, to all of us. Stochastic Processes contains 41 articles related to and frequently influ enced by Kallianpur's work. We regret that space considerations prevented us from including contributions from his numerous colleagues (at North Carolina, lSI, Minnesota, Michigan), former students, co-authors and other eminent scientists whose work is akin to Kallianpur's. This would have taken several more volumes! All articles have been refereed, and for their valuable assistance in this we thank many of the contributing authors, as well as: R. Bradley, M.H.A. Davis, R. Davis, J. Hawkins, J. Horowitz, C. Houdre, N.C. Jain, C. Ji, P. Kokoszka, T. Kurtz, K.S. Lau, W. Linde, D. Monrad, D. Stroook, D. Surgailis and S. Yakowitz. We also thank June Maxwell for editorial assistance, Peggy Ravitch for help with the production of the volume, and Lisa Brooks for secretarial assistance. Finally, we are indebted to Dr. Martin Gilchrist, the Statistics editor, and the Springer editorial board for their excellent cooperation and enthusiastic support throughout this project.

This volume celebrates the many contributions which Gopinath Kallianpur has made to probability and statistics. It comprises 40 chapters which taken together survey the wide sweep of ideas which have been influenced by Professor Kallianpur's writing and research.

A remark on the support of cadlag processes.- Large deviation results for branching processes.- Random iterations of two quadratic maps.- Zero-one law for semigroups of measures on groups.- Multiplicity properties of stationary second order random fields.- Multiple time scale analysis of hierarchically interacting systems.- Feynman's operational calculus as a generalized path integral.- Forward and backward equations for an adjoint process.- The transition function of a measure-valued branching diffusion with immigration.- Scattering theory for unitary cocycles.- Sur les variations des fonctions aléatoires Gaussiennes.- Random allocation methods in an epidemic model.- On Hellinger transforms for solutions of martingale problems.- The homogeneous chaos over compact Lie groups.- Asymptotics for two-dimensional anisotropic random walks.- A role of the Lévy Laplacian in the causal calculus of generalized white noise functionals.- On the approximation of multiple Stratonovich integrals.- Two examples of parameter estimation for stochastic partial differential equations.- Computer simulation of ?-stable Ornstein-Uhlenbeck processes.- Some linear random functional characterized by Lp-symmetries.- Higher order approximate Markov chain filters.- Fourier transform and cylindrical Hida distributions.- Representation and stability of nonlinear filters associated with Gaussian noises.- On central limit theory for families of strongly mixing additive random functions.- Positive generalized functions on infinite dimensional space.- Strong solutions of stochastic bilinear equations with anticipating drift in the first Wiener chaos.- Structure of periodically distributed stochastic sequences.- Markov property of measure-indexed Gaussian random fields.- Relative entropy as a countably additive measure.- Probability bounds, multivariate normal distribution and an integro-diflferential inequality for random vectors.- On the gauge for the third boundary value problem.- A note on prediction and an autoregressive sequence.- On generalized stochastic partial differential equations.- Examples of self similar stable processes.- Green operators of absorbing Levy processes on the half line.- Moments of sums of independent random variables.- Relative entropy and hydrodynamic limits.- Donsker's ?-function and its applications in the theory of white noise analysis.- A fractional calculus on Wiener space.- Inequalities for products of white noise functionals.- A note on the consistency of M-estimates in linear models.