An AMS special meeting in honour of a distinguished probabilist, M. M. Rao, was held in 2002, and the present volume contains most of the talks given at the meeting. More than 20 original papers reflect Rao's broad scientific interests in probability, stochastic processes, Banach space theory, measure theory and (stochastic) differential equations. His introductory paper Stochastic analysis and function spaces with a broad bibliography serves and will serve as an excellent survey of recent research. Contributed papers discuss the following topics: Sinkhorn balancing to counting problem (Beichl, Sullivan); Nonlinear filtering of an equation with Ornstein-Uhlenbeck noise (Bhatt, Rajput, Xiong); Hyperfunctionals and generalized distributions (Burgin); Process measures and their stochastic integrals (Dincunuleanu); Invariant sets for nonlinear operators (G. Goldstein, J. A. Goldstein); Immigration-emigration catastrophe model (Green); Approximating scale mixtures (Hamdan, Nolan); Cyclostationary arrays (Hurd, Koski); Operators and pseudoergodicity in information channels (Kakihara); Birth-deaths processes (Krinik, Mortensen, Rubino); Integrated Gaussian processes (Lukič); Prediction for multidimensional harmonizable processes (Mehlman); Double-level averaging on a stratified space (O'Bryant); Optimal asset allocation with stable distributed returns (Rachev, Ortobelli, Schwartz); Computations for nosquare constants of Orlicz spaces (Ren); Asymptotically stationary processes (Screiber); Superlinearity and Sobolev spaces (Shapiro); Doubly stochastic operators, Birkhoff's problem no. 111 (King, Shiflet); Harmonizable isotropic random fields (Swift); Geographically-uniform coevolution (Switkes, Moody); Time delay oscillators and delay couplings (Wirkus). The volume is completed with a bibliography and biography of M. M. Rao. A remarkable collection of personal reminiscences (written by his former students) adds a human dimension to this fine book.