This textbook offers a compact introductory course on Malliavin calculus, an active and powerful area of research. It covers recent applications, including density formulas, regularity of probability laws, central and non-central limit theorems for Gaussian functionals, convergence of densities and non-central limit theorems for the local time of Brownian motion. The book also includes a self-contained presentation of Brownian motion and stochastic calculus, as well as Lévy processes and stochastic calculus for jump processes. Accessible to non-experts, the book can be used by graduate students and researchers to develop their mastery of the core techniques necessary for further study.
High-dimensional probability offers insight into the behavior of random vectors, random matrices, random subspaces, and objects used to quantify uncertainty in high dimensions. Drawing on ideas from probability, analysis, and geometry, it lends itself to applications in mathematics, statistics, theoretical computer science, signal processing, optimization, and more. It is the first to integrate theory, key tools, and modern applications of high-dimensional probability. Concentration inequalities form the core, and it covers both classical results such as Hoeffding's and Chernoff's inequalities and modern developments such as the matrix Bernstein's inequality. It then introduces the powerful methods based on stochastic processes, including such tools as Slepian's, Sudakov's, and Dudley's inequalities, as well as generic chaining and bounds based on VC dimension. A broad range of illustrations is embedded throughout, including classical and modern results for covariance estimation, clust
Geometry and Martingales in Banach Spaces provides a compact exposition of the results explaining the interrelations existing between the metric geometry of Banach spaces and the theory of martingales
This textbook addresses postgraduate students in applied mathematics, probability, and statistics, as well as computer scientists, biologists, physicists and economists, who are seeking a rigorous int
This book provides a new analytical approach for dynamic data repeatedly measured from multiple subjects over time. Random effects account for differences across subjects. Auto-regression in response
This monograph develops the Gaussian functional capacity theory with applications to restricting the Gaussian Campanato/Sobolev/BV space. Included in the text is a new geometric characterization of th
Written by the leading expert in the field, this text reviews the major new developments in envelope models and methods An Introduction to Envelopes provides an overview of the theory and method
Oncology is a rapidly developing area in medical science. A significant investment in terms of costs, resources and time is required for oncology drug development. Understanding of the challenges at a
This book provides an accessible presentation of concepts from probability theory, statistical methods, the design of experiments and statistical quality control. It is shaped by the experience of the
Presents a unified approach to parametric estimation, confidence intervals, hypothesis testing, and statistical modeling, which are uniquely based on the likelihood function This book addresses mathem
This book brings together a variety of probability applications through entertaining stories that will appeal to a broad readership. What are the best stopping rules for the dating problem? What can B
This is an introductory text on a broad class of statistical estimators that are minimizers of convex functions. It covers the basics of U-statistics and Mm-estimators and develops their asymptotic pr
This book collects important advances in methodology and data analysis for directional statistics. It is the companion book of the more theoretical treatment presented in Modern Directional Statistics
Computational Analysis and Understanding of Natural Languages: Principles, Methods and Applications, Volume 38, the latest release in this monograph that provides a cohesive and integrated exposition
A guide to modern optimization applications and techniques in newly emerging areas spanning optimization, data science, machine intelligence, engineering, and computer sciences Optimization Techn
Roxy Peck and Tom Short's STATISTICS COMPANION supports your success in Statistics by providing a review of the necessary Statistics-specific mathematics, study skills, and Statistics-language content
Enables readers to start doing actual data analysis fast for a truly hands-on learning experienceThis concise and very easy-to-use primer introduces readers to a host of computational tools useful for
An essential guide to two burgeoning topics in machine learning – classification trees and ensemble learning Ensemble Classification Methods with Applications in R introduces the concepts a
