Topics in Stochastic Analysis and Nonparametric Estimation

ISBN-13: 9781441925817 / Angielski / Miękka / 2011 / 214 str.

Pao-Liu Chow; Boris S. Mordukhovich; G. George Yin

Opis

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."

Spis treści

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.

Blurb

To assess the past achievement and to provide a road map for future research, an IMA participating institution conference entitled "Conference on Asymptotic Analysis in Stochastic Processes, Nonparametric Estimation, and Related Problems" was held at Wayne State University, September 15-17, 2006. This conference was also held to honor Professor Rafail Z. Khasminskii for his fundamental contributions to many aspects of stochastic processes and nonparametric estimation theory on the occasion of his seventy-fifth birthday. It assembled an impressive list of invited speakers, who are renowned leaders in the fields of probability theory, stochastic processes, stochastic differential equations, as well as in the nonparametric estimation theory, and related fields. A number of invited speakers were early developers of the fields of probability and stochastic processes, establishing the foundation of the Modern probability theory. After the conference, to commemorate this special event, an IMA volume dedicated to Professor Rafail Z. Khasminskii was put together. It consists of nine papers on various topics in probability and statistics. They include authoritative expositions as well as significant research papers of current interest. It is conceivable that the volume will have a lasting impact on the further development of stochastic analysis and nonparametric estimation.