Topics in Stochastic Analysis and Nonparametric Estimation

This IMA Volume in Mathematics and its Applications TOPICS IN STOCHASTIC ANALYSIS AND NONPARAMETRIC ESTIMATION contains papers that were presented at the IMA Participating Institution conference on "Asymptotic Analysis in Stochastic Processes, Nonparamet­ ric Estimation, and Related Problems" held on September 15-17, 2006 at Wayne State University. The conference, which was one of approximately ten selected each year for partial support by the IMA through its affiliates program, was dedicated to Professor Rafail Z. Khasminskii on the occasion th of his 75 birthday, in recognition of his profound contributions to the field of stochastic processes and nonparametric estimation theory. We are grateful to the participants and, especially, to the conference organizers, for making the event so successful. Pao-Liu Chow, Boris Mor­ dukhovich, and George Yin of the Department of Mathematics at Wayne State University did a superb job organizing this first-rate event and in editing these proceedings. We take this opportunity to thank the Nation al Science Foundation for its support of the IMA.

Asymptotic Analysis Involving Stochastic Differential Equations.- Some Recent Results on Averaging Principle.- Cramer’s Theorem for Nonnegative Multivariate Point Processes with Independent Increments.- On Bounded Solutions of the Balanced Generalized Pantograph Equation.- Numerical Methods for Non-Zero-Sum Stochastic Differential Games: Convergence of the Markov Chain Approximation Method.- Nonparametric Estimation.- On the Estimation of an Analytic Spectral Density Outside of the Observation Band.- On Oracle Inequalities Related to High Dimensional Linear Models.- Hypothesis Testing under Composite Functions Alternative.- Stochastic Partial Differential Equations.- On Parabolic Pdes and Spdes in Sobolev Spaces W P 2 without and with Weights.- Stochastic Parabolic Equations of Full Second Order.