Abstract homotopy theory is based on the observation that analogues of much of topological homotopy theory and simple homotopy theory exist in many other categories, such as spaces over a fixed base, groupoids, chain complexes and module categories. Studying categorical versions of homotopy structur
Abstract homotopy and simple homotopy theory
โ Scribed by Klaus Heiner Kamps; T Porter
- Publisher
- World Scientific
- Year
- 1997
- Tongue
- English
- Leaves
- 471
- Category
- Library
No coin nor oath required. For personal study only.
โฆ Synopsis
This book provides a research-expository treatment of infinite-dimensional nonstationary stochastic processes or times series. Stochastic measures and scalar or operator bimeasures are fully discussed to develop integral representations of various classes of nonstationary processes such as harmonizable, "V"-bounded, Cramer and Karhunen classes and also the stationary class. Emphasis is on the use of functional, harmonic analysis as well as probability theory. Applications are made from the probabilistic and statistical points of view to prediction problems, Kalman filter, sampling theorems and strong laws of large numbers. Readers may find that the covariance kernel analysis is emphasized and it reveals another aspect of stochastic processes. This book is intended not only for probabilists and statisticians, but also for communication engineers
๐ SIMILAR VOLUMES
The purpose of this monograph, which is aimed at the graduate level and beyond, is to obtain a deeper understanding of Quillen's model categories. A model category is a category together with three distinguished classes of maps, called weak equivalences, cofibrations, and fibrations. Model categorie
The author, a leading figure in algebraic topology, provides a modern treatment of a long established set of questions in this important research area. The book's principal objective--and main result--is the classification theorem on k-variants and boundary invariants, which supplement the classical