Series: Stochastic Modelling and Applied Probability , Vol. 28Series: Stochastic Modelling and Applied Probability , Vol. 28
2006, XX, 301 p., 17 illus., Hardcover
ISBN: 0-387-29166-0
About this book
This book is a prototype providing new insight into Markovian
dependence via the cycle decompositions. It presents a systematic
account of a class of stochastic processes known as cycle (or
circuit) processes - so-called because they may be defined by
directed cycles. These processes have special and important
properties through the interaction between the geometric
properties of the trajectories and the algebraic characterization
of the Markov process. An important application of this approach
is the insight it provides to electrical networks and the duality
principle of networks. In particular, it provides an entirely new
approach to infinite electrical networks and their applications
in topics as diverse as random walks, the classification of
Riemann surfaces, and to operator theory.
The second edition of this book adds new advances to many
directions, which reveal wide-ranging interpretations of the
cycle representations like homologic decompositions,
orthogonality equations, Fourier series, semigroup equations, and
disintegration of measures. The versatility of these
interpretations is consequently motivated by the existence of
algebraic-topological principles in the fundamentals of the cycle
representations. This book contains chapter summaries as well as
a number of detailed illustrations.
Table of contents
Preface.- Acknowledgements.- Preface to the Second Edition.-
Directed Circuits.- Genesis of Markov Chains by Circuits: The
Circuit Chains.- Cycle Representations of Recurrent Denumerable
Markov Chains.- Circuit Representations of Finite Recurrent
Markov Chains.- Continuous Parameter Circuit Processes with
Finite State Space.- Spectral Theory of Circuit Processes.-
Higher Order Circuit Processes.- Cycloid Markov Processes.-
Markov Processes on Banach Spaces on Cycles.- The Cycle Measures.-
Wide-Ranging Interpretations of the Cycle Processes.- Stochastic
Properties in Terms of Circuits.- Levy's Theorem Concerning
Positiveness of Transition Probabilities.- The Rotational Theory
of Markov Processes.
Series: Lecture Notes in Statistics , Vol. 186
2006, XIV, 410 p., 101 illus., Softcover
ISBN: 0-387-31102-5
About this book
Time series play a crucial role in modern economies at all levels
of activity and are used by decision makers to plan for a better
future. Before publication time series are subject to statistical
adjustments and this is the first statistical book to
systematically deal with the methods most often applied for such
adjustments. Regression-based models are emphasized because of
their clarity, ease of application, and superior results. Each
topic is illustrated with real case examples. In order to
facilitate understanding of their properties and limitations of
the methods discussed a real data example is followed throughout
the book.
Table of contents
Introduction.- The Components of Time Series.- The Cholette-Dagum
Regression-Based Benchmarking Method--The Additive Model.-
Covariance Matrices for Benchmarking and Reconciliation Methods.-
The Cholette-Dagum Regression-Based Benchmarking Method.--Multiplicative
Model.- The Denton Method and its Variants.- Interpolation,
Temporal Distribution and Extrapolation.- Signal Extraction and
Benchmarking.- Calendarization.- Unified Regression-Based
Framework for Signal Extraction, Benchmarking and Interpolation.-
Reconciliation and Balancing Systems of Time Series.- Reconciling
One-Way Classified Systems of Time Series.- Reconciling the
Marginal Totals of Two-Way Classified Systems of Series.-
Reconciling Two-Way Classified Systems of Time Series.
Series: Lecture Notes in Statistics , Vol. 88
3rd ed., 2006, X, 222 p., Softcover
ISBN: 0-387-31409-1
About this book
This book presents theoretical results relevant to Edgeworth and
saddlepoint expansions to densities and distribution functions.
It provides examples of their application in some simple and a
few complicated settings, along with numerical, as well as
asymptotic, assessments of their accuracy. Variants on these
expansions, including much of modern likelihood theory, are
discussed and applications to lattice distribtuions are
extensively treated. This book is intended primarily for advanced
graduate students and researchers in the field needing a
collection of core results in a uniform notation, with
bibliographical references to further examples and applications.
It assumes familiarity with real analysis, vector calculus, and
complex analysis. This third edition features an expansion of the
material on the Blackwell approximation and an expansion of the
discussions on saddlepoint approximation. John E. Kolassa is
Assistant Professor of Biostatistics at the University of
Rochester.
Table of contents
Asymptotics in General.-. Characteristic Functions and the Berry-Esseen
Theorem.- Edgeworth Series.- Saddlepoint Series for Densities.-
Saddlepoint Series for Distribution Functions.- Multivariate
Expansions.- Conditional Distribution Approximations.-
Applications to Likelihood Ratio and Maximum Likelihood
Statistics.- Other Topics.- Computational Aids.
2006, XX, 420 p., 7 illus., Hardcover
ISBN: 0-387-29742-1
About this book
This book provides a panoramic view of theory and applications of
Ageing and Dependence in the use of mathematical methods in
reliability and survival analysis. Ageing and dependence are
important characteristics in reliability and survival analysis.
They affect decisions with regard to maintenance, repair/replacement,
price setting, warranties, medical studies, and other areas. Most
of the works containing the topics covered here are theoretical
in nature. However, this book offers applications, exercises, and
examples. It serves as a reference for professors and researchers
involved in reliability and survival analysis.
Table of contents
Series: Lecture Notes in Economics and Mathematical Systems , Vol. 574
2006, XIV, 182 p., 55 illus., Softcover
ISBN: 3-540-33229-4
About this book
The integration of product recovery into regular production
processes enables new opportunities for cost savings. It also
yields new challenges for inventory management because there are
two sources to satisfy product requirements which need to be
coordinated by additionally taking into account limited
availability of used products. In case of a dynamic planning
situation, for instance when dealing with seasonality or the
product life cycle, new motives for keeping stock arise. The work
aims to identify those motives and to describe their effects by
using methods of optimal control theory.
Table of contents
Introduction.- A Basic Quantitative Model.- On the Effects of
Capacity Constraints in Product Recovery.- Knowledge Acquisition
and Product Recovery.- Technology Selection in the Context of
Reverse Logistics.- Conclusions