Ebook: Topics in Stochastic Analysis and Nonparametric Estimation

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.

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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.

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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.
Content:
Front Matter....Pages i-xi
Front Matter....Pages 1-1
Some Recent Results on Averaging Principle....Pages 1-19
Cramer’s Theorem for Nonnegative Multivariate Point Processes with Independent Increments....Pages 21-28
On Bounded Solutions of the Balanced Generalized Pantograph Equation....Pages 29-49
Numerical Methods for Non-Zero-Sum Stochastic Differential Games: Convergence of the Markov Chain Approximation Method....Pages 51-84
Front Matter....Pages 85-85
On the Estimation of an Analytic Spectral Density Outside of the Observation Band....Pages 85-103
On Oracle Inequalities Related to High Dimensional Linear Models....Pages 105-122
Hypothesis Testing under Composite Functions Alternative....Pages 123-150
Front Matter....Pages 151-151
On Parabolic Pdes and Spdes in Sobolev Spaces W P 2 without and with Weights....Pages 151-197
Stochastic Parabolic Equations of Full Second Order....Pages 199-210

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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.
Content:
Front Matter....Pages i-xi
Front Matter....Pages 1-1
Some Recent Results on Averaging Principle....Pages 1-19
Cramer’s Theorem for Nonnegative Multivariate Point Processes with Independent Increments....Pages 21-28
On Bounded Solutions of the Balanced Generalized Pantograph Equation....Pages 29-49
Numerical Methods for Non-Zero-Sum Stochastic Differential Games: Convergence of the Markov Chain Approximation Method....Pages 51-84
Front Matter....Pages 85-85
On the Estimation of an Analytic Spectral Density Outside of the Observation Band....Pages 85-103
On Oracle Inequalities Related to High Dimensional Linear Models....Pages 105-122
Hypothesis Testing under Composite Functions Alternative....Pages 123-150
Front Matter....Pages 151-151
On Parabolic Pdes and Spdes in Sobolev Spaces W P 2 without and with Weights....Pages 151-197
Stochastic Parabolic Equations of Full Second Order....Pages 199-210
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