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Author: Dariusz Buraczewski Publisher: Springer ISBN: 3319296795 Category : Mathematics Languages : en Pages : 325
Book Description
In this monograph the authors give a systematic approach to the probabilistic properties of the fixed point equation X=AX+B. A probabilistic study of the stochastic recurrence equation X_t=A_tX_{t-1}+B_t for real- and matrix-valued random variables A_t, where (A_t,B_t) constitute an iid sequence, is provided. The classical theory for these equations, including the existence and uniqueness of a stationary solution, the tail behavior with special emphasis on power law behavior, moments and support, is presented. The authors collect recent asymptotic results on extremes, point processes, partial sums (central limit theory with special emphasis on infinite variance stable limit theory), large deviations, in the univariate and multivariate cases, and they further touch on the related topics of smoothing transforms, regularly varying sequences and random iterative systems. The text gives an introduction to the Kesten-Goldie theory for stochastic recurrence equations of the type X_t=A_tX_{t-1}+B_t. It provides the classical results of Kesten, Goldie, Guivarc'h, and others, and gives an overview of recent results on the topic. It presents the state-of-the-art results in the field of affine stochastic recurrence equations and shows relations with non-affine recursions and multivariate regular variation.
Author: Dariusz Buraczewski Publisher: Springer ISBN: 3319296795 Category : Mathematics Languages : en Pages : 325
Book Description
In this monograph the authors give a systematic approach to the probabilistic properties of the fixed point equation X=AX+B. A probabilistic study of the stochastic recurrence equation X_t=A_tX_{t-1}+B_t for real- and matrix-valued random variables A_t, where (A_t,B_t) constitute an iid sequence, is provided. The classical theory for these equations, including the existence and uniqueness of a stationary solution, the tail behavior with special emphasis on power law behavior, moments and support, is presented. The authors collect recent asymptotic results on extremes, point processes, partial sums (central limit theory with special emphasis on infinite variance stable limit theory), large deviations, in the univariate and multivariate cases, and they further touch on the related topics of smoothing transforms, regularly varying sequences and random iterative systems. The text gives an introduction to the Kesten-Goldie theory for stochastic recurrence equations of the type X_t=A_tX_{t-1}+B_t. It provides the classical results of Kesten, Goldie, Guivarc'h, and others, and gives an overview of recent results on the topic. It presents the state-of-the-art results in the field of affine stochastic recurrence equations and shows relations with non-affine recursions and multivariate regular variation.
Author: Mark M. Meerschaert Publisher: Walter de Gruyter GmbH & Co KG ISBN: 3110559145 Category : Mathematics Languages : en Pages : 421
Book Description
Fractional calculus is a rapidly growing field of research, at the interface between probability, differential equations, and mathematical physics. It is used to model anomalous diffusion, in which a cloud of particles spreads in a different manner than traditional diffusion. This monograph develops the basic theory of fractional calculus and anomalous diffusion, from the point of view of probability. In this book, we will see how fractional calculus and anomalous diffusion can be understood at a deep and intuitive level, using ideas from probability. It covers basic limit theorems for random variables and random vectors with heavy tails. This includes regular variation, triangular arrays, infinitely divisible laws, random walks, and stochastic process convergence in the Skorokhod topology. The basic ideas of fractional calculus and anomalous diffusion are closely connected with heavy tail limit theorems. Heavy tails are applied in finance, insurance, physics, geophysics, cell biology, ecology, medicine, and computer engineering. The goal of this book is to prepare graduate students in probability for research in the area of fractional calculus, anomalous diffusion, and heavy tails. Many interesting problems in this area remain open. This book will guide the motivated reader to understand the essential background needed to read and unerstand current research papers, and to gain the insights and techniques needed to begin making their own contributions to this rapidly growing field.
Author: Howard M. Taylor Publisher: Academic Press ISBN: 1483269272 Category : Mathematics Languages : en Pages : 410
Book Description
An Introduction to Stochastic Modeling provides information pertinent to the standard concepts and methods of stochastic modeling. This book presents the rich diversity of applications of stochastic processes in the sciences. Organized into nine chapters, this book begins with an overview of diverse types of stochastic models, which predicts a set of possible outcomes weighed by their likelihoods or probabilities. This text then provides exercises in the applications of simple stochastic analysis to appropriate problems. Other chapters consider the study of general functions of independent, identically distributed, nonnegative random variables representing the successive intervals between renewals. This book discusses as well the numerous examples of Markov branching processes that arise naturally in various scientific disciplines. The final chapter deals with queueing models, which aid the design process by predicting system performance. This book is a valuable resource for students of engineering and management science. Engineers will also find this book useful.
Author: Hideaki Aoyama Publisher: Cambridge University Press ISBN: 1108225802 Category : Science Languages : en Pages : 438
Book Description
The concepts of statistical physics and big data play an important role in the evidence-based analysis and interpretation of macroeconomic principles. The techniques of complex networks, big data, and statistical physics are useful to understand theories of economic systems, and the authors have applied these to understand the intricacies of complex macroeconomic problems. Recent research work using tools and techniques of big data, statistical physics, complex networks, and statistical science is covered, and basic graph algorithms and statistical measures of complex networks are described. The application of big data and statistical physics tools to assess price dynamics, inflation, systemic risks, and productivity is discussed. Chapter-end summary and numerical problems are provided to reinforce understanding of concepts.
Author: Torben Gustav Andersen Publisher: Springer Science & Business Media ISBN: 3540712976 Category : Business & Economics Languages : en Pages : 1045
Book Description
The Handbook of Financial Time Series gives an up-to-date overview of the field and covers all relevant topics both from a statistical and an econometrical point of view. There are many fine contributions, and a preamble by Nobel Prize winner Robert F. Engle.
Author: Quan-Lin Li Publisher: Springer Science & Business Media ISBN: 364211492X Category : Mathematics Languages : en Pages : 693
Book Description
"Constructive Computation in Stochastic Models with Applications: The RG-Factorizations" provides a unified, constructive and algorithmic framework for numerical computation of many practical stochastic systems. It summarizes recent important advances in computational study of stochastic models from several crucial directions, such as stationary computation, transient solution, asymptotic analysis, reward processes, decision processes, sensitivity analysis as well as game theory. Graduate students, researchers and practicing engineers in the field of operations research, management sciences, applied probability, computer networks, manufacturing systems, transportation systems, insurance and finance, risk management and biological sciences will find this book valuable. Dr. Quan-Lin Li is an Associate Professor at the Department of Industrial Engineering of Tsinghua University, China.
Author: Victor Yu Korolev Publisher: Walter de Gruyter ISBN: 9789067644495 Category : Plasma turbulence Languages : en Pages : 424
Book Description
The series is devoted to the publication of high-level monographs and surveys which cover the whole spectrum of probability and statistics. The books of the series are addressed to both experts and advanced students.
Author: Tom Gedeon Publisher: Springer Nature ISBN: 3030367088 Category : Computers Languages : en Pages : 790
Book Description
The three-volume set of LNCS 11953, 11954, and 11955 constitutes the proceedings of the 26th International Conference on Neural Information Processing, ICONIP 2019, held in Sydney, Australia, in December 2019. The 173 full papers presented were carefully reviewed and selected from 645 submissions. The papers address the emerging topics of theoretical research, empirical studies, and applications of neural information processing techniques across different domains. The first volume, LNCS 11953, is organized in topical sections on adversarial networks and learning; convolutional neural networks; deep neural networks; feature learning and representation; human centred computing; human centred computing and medicine; hybrid models; and artificial intelligence and cybersecurity.
Author: Pierre Delhaes Publisher: John Wiley & Sons ISBN: 1119427967 Category : Technology & Engineering Languages : en Pages : 232
Book Description
A thermodynamic system is defined according to its environment and its compliance. This book promotes the classification of materials from generalized thermodynamics outside the equilibrium state and not solely according to their chemical origin. The author goes beyond standard classification of materials and extends it to take into account the living, ecological, economic and financial systems in which they exist: all these systems can be classified according to their deviation from an ideal situation of thermodynamic equilibrium. The concepts of dynamic complexity and hierarchy, emphasizing the crucial role played by cycles and rhythms, then become fundamental. Finally, the limitations of the uniqueness of this description that depend on thermodynamic foundations based on the concepts of energy and entropy are discussed in relation to the cognitive sciences.
Author: Dariusz Buraczewski
Author: Dariusz Buraczewski
Author: Mark M. Meerschaert
Author: Howard M. Taylor
Author: Hideaki Aoyama
Author: Torben Gustav Andersen
Author: Quan-Lin Li
Author: Thomas Mikosch
Author: Victor Yu Korolev
Author: Tom Gedeon
Author: Pierre Delhaes