Compound Renewal Processes

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Compound Renewal Processes

A. A. Borovkov
Compound Renewal Processes Book PDF

Author : A. A. Borovkov
Publisher : Cambridge University Press
Page : 128 pages
File Size : 52,6 Mb
Release : 2022-06-30
Category : Mathematics
ISBN : 9781009115605

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Compound Renewal Processes by A. A. Borovkov Pdf

Compound renewal processes (CRPs) are among the most ubiquitous models arising in applications of probability. At the same time, they are a natural generalization of random walks, the most well-studied classical objects in probability theory. This monograph, written for researchers and graduate students, presents the general asymptotic theory and generalizes many well-known results concerning random walks. The book contains the key limit theorems for CRPs, functional limit theorems, integro-local limit theorems, large and moderately large deviation principles for CRPs in the state space and in the space of trajectories, including large deviation principles in boundary crossing problems for CRPs, with an explicit form of the rate functionals, and an extension of the invariance principle for CRPs to the domain of moderately large and small deviations. Applications establish the key limit laws for Markov additive processes, including limit theorems in the domains of normal and large deviations.

Stochastic Processes in Science, Engineering and Finance

Frank Beichelt
Stochastic Processes in Science Engineering and Finance Book PDF

Author : Frank Beichelt
Publisher : CRC Press
Page : 438 pages
File Size : 40,8 Mb
Release : 2006-02-22
Category : Mathematics
ISBN : 142001045X

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Stochastic Processes in Science, Engineering and Finance by Frank Beichelt Pdf

This book presents a self-contained introduction to stochastic processes with emphasis on their applications in science, engineering, finance, computer science, and operations research. It provides theoretical foundations for modeling time-dependent random phenomena in these areas and illustrates their application by analyzing numerous practical examples. The treatment assumes few prerequisites, requiring only the standard mathematical maturity acquired by undergraduate applied science students. It includes an introductory chapter that summarizes the basic probability theory needed as background. Numerous exercises reinforce the concepts and techniques discussed and allow readers to assess their grasp of the subject. Solutions to most of the exercises are provided in an appendix. While focused primarily on practical aspects, the presentation includes some important proofs along with more challenging examples and exercises for those more theoretically inclined. Mastering the contents of this book prepares readers to apply stochastic modeling in their own fields and enables them to work more creatively with software designed for dealing with the data analysis aspects of stochastic processes.

Applied Probability and Stochastic Processes

Frank Beichelt
Applied Probability and Stochastic Processes Book PDF

Author : Frank Beichelt
Publisher : CRC Press
Page : 562 pages
File Size : 47,7 Mb
Release : 2018-09-03
Category : Business & Economics
ISBN : 9781315362571

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Applied Probability and Stochastic Processes by Frank Beichelt Pdf

Applied Probability and Stochastic Processes, Second Edition presents a self-contained introduction to elementary probability theory and stochastic processes with a special emphasis on their applications in science, engineering, finance, computer science, and operations research. It covers the theoretical foundations for modeling time-dependent random phenomena in these areas and illustrates applications through the analysis of numerous practical examples. The author draws on his 50 years of experience in the field to give your students a better understanding of probability theory and stochastic processes and enable them to use stochastic modeling in their work. New to the Second Edition Completely rewritten part on probability theory—now more than double in size New sections on time series analysis, random walks, branching processes, and spectral analysis of stationary stochastic processes Comprehensive numerical discussions of examples, which replace the more theoretically challenging sections Additional examples, exercises, and figures Presenting the material in a student-friendly, application-oriented manner, this non-measure theoretic text only assumes a mathematical maturity that applied science students acquire during their undergraduate studies in mathematics. Many exercises allow students to assess their understanding of the topics. In addition, the book occasionally describes connections between probabilistic concepts and corresponding statistical approaches to facilitate comprehension. Some important proofs and challenging examples and exercises are also included for more theoretically interested readers.

Pseudo-Regularly Varying Functions and Generalized Renewal Processes

Valeriĭ V. Buldygin,Karl-Heinz Indlekofer,Oleg I. Klesov,Josef G. Steinebach
Pseudo Regularly Varying Functions and Generalized Renewal Processes Book PDF

Author : Valeriĭ V. Buldygin,Karl-Heinz Indlekofer,Oleg I. Klesov,Josef G. Steinebach
Publisher : Springer
Page : 482 pages
File Size : 55,5 Mb
Release : 2018-10-12
Category : Mathematics
ISBN : 9783319995373

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Pseudo-Regularly Varying Functions and Generalized Renewal Processes by Valeriĭ V. Buldygin,Karl-Heinz Indlekofer,Oleg I. Klesov,Josef G. Steinebach Pdf

One of the main aims of this book is to exhibit some fruitful links between renewal theory and regular variation of functions. Applications of renewal processes play a key role in actuarial and financial mathematics as well as in engineering, operations research and other fields of applied mathematics. On the other hand, regular variation of functions is a property that features prominently in many fields of mathematics. The structure of the book reflects the historical development of the authors’ research work and approach – first some applications are discussed, after which a basic theory is created, and finally further applications are provided. The authors present a generalized and unified approach to the asymptotic behavior of renewal processes, involving cases of dependent inter-arrival times. This method works for other important functionals as well, such as first and last exit times or sojourn times (also under dependencies), and it can be used to solve several other problems. For example, various applications in function analysis concerning Abelian and Tauberian theorems can be studied as well as those in studies of the asymptotic behavior of solutions of stochastic differential equations. The classes of functions that are investigated and used in a probabilistic context extend the well-known Karamata theory of regularly varying functions and thus are also of interest in the theory of functions. The book provides a rigorous treatment of the subject and may serve as an introduction to the field. It is aimed at researchers and students working in probability, the theory of stochastic processes, operations research, mathematical statistics, the theory of functions, analytic number theory and complex analysis, as well as economists with a mathematical background. Readers should have completed introductory courses in analysis and probability theory.

Level-Crossing Problems and Inverse Gaussian Distributions

Vsevolod K. Malinovskii
Level Crossing Problems and Inverse Gaussian Distributions Book PDF

Author : Vsevolod K. Malinovskii
Publisher : CRC Press
Page : 259 pages
File Size : 48,5 Mb
Release : 2021-07-26
Category : Mathematics
ISBN : 9781000392944

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Level-Crossing Problems and Inverse Gaussian Distributions by Vsevolod K. Malinovskii Pdf

Level-Crossing Problems and Inverse Gaussian Distributions: Closed-Form Results and Approximations focusses on the inverse Gaussian approximation for the distribution of the first level-crossing time in a shifted compound renewal process framework. This approximation, whose name was coined by the author, is a successful competitor of the normal (or Cramér's), diffusion, and Teugels’ approximations, being a breakthrough in its conditions and accuracy. Since such approximations underlie numerous applications in risk theory, queueing theory, reliability theory, and mathematical theory of dams and inventories, this book is of interest not only to professional mathematicians, but also to physicists, engineers, and economists. People from industry, with a theoretical background in level-crossing problems, e.g., from the insurance industry, can also benefit from reading this book. Features: Primarily aimed at researchers and postgraduates, but may be of interest to some professionals working in related fields, such as the insurance industry Suitable for advanced courses in Applied Probability and, as a supplementary reading, for basic courses in Applied Probability

Fractional Dynamics

Joseph Klafter,S. C. Lim,Ralf Metzler
Fractional Dynamics Book PDF

Author : Joseph Klafter,S. C. Lim,Ralf Metzler
Publisher : World Scientific
Page : 530 pages
File Size : 45,5 Mb
Release : 2012
Category : Mathematics
ISBN : 9789814340588

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Fractional Dynamics by Joseph Klafter,S. C. Lim,Ralf Metzler Pdf

This volume provides the latest developments in the field of fractional dynamics, which covers fractional (anomalous) transport phenomena, fractional statistical mechanics, fractional quantum mechanics and fractional quantum field theory. The contributors are selected based on their active and important contributions to their respective topics. This volume is the first of its kind that covers such a comprehensive range of topics in fractional dynamics. It will point out to advanced undergraduate and graduate students, and young researchers the possible directions of research in this subject. In addition to those who intend to work in this field and those already in the field, this volume will also be useful for researchers not directly involved in the field, but want to know the current status and trends of development in this subject. This latter group includes theoretical chemists, mathematical biologists and engineers.

Stochastic Storage Processes

N.U. Prabhu
Stochastic Storage Processes Book PDF

Author : N.U. Prabhu
Publisher : Springer Science & Business Media
Page : 218 pages
File Size : 41,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461217428

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Stochastic Storage Processes by N.U. Prabhu Pdf

A self-contained treatment of stochastic processes arising from models for queues, insurance risk, and dams and data communication, using their sample function properties. The approach is based on the fluctuation theory of random walks, L vy processes, and Markov-additive processes, in which Wiener-Hopf factorisation plays a central role. This second edition includes results for the virtual waiting time and queue length in single server queues, while the treatment of continuous time storage processes is thoroughly revised and simplified. With its prerequisite of a graduate-level course in probability and stochastic processes, this book can be used as a text for an advanced course on applied probability models.

Safety, Reliability and Risk Analysis

Sebastian Martorell,Carlos Guedes Soares,Julie Barnett
Safety Reliability and Risk Analysis Book PDF

Author : Sebastian Martorell,Carlos Guedes Soares,Julie Barnett
Publisher : CRC Press
Page : 3512 pages
File Size : 48,7 Mb
Release : 2008-09-10
Category : Technology & Engineering
ISBN : 9781482266481

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Safety, Reliability and Risk Analysis by Sebastian Martorell,Carlos Guedes Soares,Julie Barnett Pdf

Safety, Reliability and Risk Analysis. Theory, Methods and Applications contains the papers presented at the joint ESREL (European Safety and Reliability) and SRA-Europe (Society for Risk Analysis Europe) Conference (Valencia, Spain, 22-25 September 2008). The book covers a wide range of topics, including: Accident and Incident Investigation; Crisi

Advances in Queueing Theory, Methods, and Open Problems

Jewgeni H. Dshalalow
Advances in Queueing Theory Methods and Open Problems Book PDF

Author : Jewgeni H. Dshalalow
Publisher : CRC Press
Page : 527 pages
File Size : 44,7 Mb
Release : 2023-07-21
Category : Business & Economics
ISBN : 9781000943290

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Advances in Queueing Theory, Methods, and Open Problems by Jewgeni H. Dshalalow Pdf

The progress of science and technology has placed Queueing Theory among the most popular disciplines in applied mathematics, operations research, and engineering. Although queueing has been on the scientific market since the beginning of this century, it is still rapidly expanding by capturing new areas in technology. Advances in Queueing provides a comprehensive overview of problems in this enormous area of science and focuses on the most significant methods recently developed. Written by a team of 24 eminent scientists, the book examines stochastic, analytic, and generic methods such as approximations, estimates and bounds, and simulation. The first chapter presents an overview of classical queueing methods from the birth of queues to the seventies. It also contains the most comprehensive bibliography of books on queueing and telecommunications to date. Each of the following chapters surveys recent methods applied to classes of queueing systems and networks followed by a discussion of open problems and future research directions. Advances in Queueing is a practical reference that allows the reader quick access to the latest methods.

Introduction to Stochastic Processes Using R

Sivaprasad Madhira,Shailaja Deshmukh
Introduction to Stochastic Processes Using R Book PDF

Author : Sivaprasad Madhira,Shailaja Deshmukh
Publisher : Springer Nature
Page : 663 pages
File Size : 50,5 Mb
Release : 2023-12-05
Category : Business & Economics
ISBN : 9789819956012

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Introduction to Stochastic Processes Using R by Sivaprasad Madhira,Shailaja Deshmukh Pdf

This textbook presents some basic stochastic processes, mainly Markov processes. It begins with a brief introduction to the framework of stochastic processes followed by the thorough discussion on Markov chains, which is the simplest and the most important class of stochastic processes. The book then elaborates the theory of Markov chains in detail including classification of states, the first passage distribution, the concept of periodicity and the limiting behaviour of a Markov chain in terms of associated stationary and long run distributions. The book first illustrates the theory for some typical Markov chains, such as random walk, gambler's ruin problem, Ehrenfest model and Bienayme-Galton-Watson branching process; and then extends the discussion when time parameter is continuous. It presents some important examples of a continuous time Markov chain, which include Poisson process, birth process, death process, birth and death processes and their variations. These processes play a fundamental role in the theory and applications in queuing and inventory models, population growth, epidemiology and engineering systems. The book studies in detail the Poisson process, which is the most frequently applied stochastic process in a variety of fields, with its extension to a renewal process. The book also presents important basic concepts on Brownian motion process, a stochastic process of historic importance. It covers its few extensions and variations, such as Brownian bridge, geometric Brownian motion process, which have applications in finance, stock markets, inventory etc. The book is designed primarily to serve as a textbook for a one semester introductory course in stochastic processes, in a post-graduate program, such as Statistics, Mathematics, Data Science and Finance. It can also be used for relevant courses in other disciplines. Additionally, it provides sufficient background material for studying inference in stochastic processes. The book thus fulfils the need of a concise but clear and student-friendly introduction to various types of stochastic processes.

Fractional Calculus

Dumitru Baleanu
Fractional Calculus Book PDF

Author : Dumitru Baleanu
Publisher : World Scientific
Page : 426 pages
File Size : 46,5 Mb
Release : 2012
Category : Mathematics
ISBN : 9789814355216

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Fractional Calculus by Dumitru Baleanu Pdf

The subject of fractional calculus and its applications (that is, convolution-type pseudo-differential operators including integrals and derivatives of any arbitrary real or complex order) has gained considerable popularity and importance during the past three decades or so, mainly due to its applications in diverse fields of science and engineering. These operators have been used to model problems with anomalous dynamics, however, they also are an effective tool as filters and controllers, and they can be applied to write complicated functions in terms of fractional integrals or derivatives of elementary functions, and so on. This book will give readers the possibility of finding very important mathematical tools for working with fractional models and solving fractional differential equations, such as a generalization of Stirling numbers in the framework of fractional calculus and a set of efficient numerical methods. Moreover, we will introduce some applied topics, in particular fractional variational methods which are used in physics, engineering or economics. We will also discuss the relationship between semi-Markov continuous-time random walks and the space-time fractional diffusion equation, which generalizes the usual theory relating random walks to the diffusion equation. These methods can be applied in finance, to model tick-by-tick (log)-price fluctuations, in insurance theory, to study ruin, as well as in macroeconomics as prototypical growth models. All these topics are complementary to what is dealt with in existing books on fractional calculus and its applications. This book was written with a trade-off in mind between full mathematical rigor and the needs of readers coming from different applied areas of science and engineering. In particular, the numerical methods listed in the book are presented in a readily accessible way that immediately allows the readers to implement them on a computer in a programming language of their choice. Numerical code is also provided.

Stochastic Processes

Narahari Umanath Prabhu
Stochastic Processes Book PDF

Author : Narahari Umanath Prabhu
Publisher : World Scientific
Page : 356 pages
File Size : 48,9 Mb
Release : 2007
Category : Mathematics
ISBN : 9789812706263

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Stochastic Processes by Narahari Umanath Prabhu Pdf

Most introductory textbooks on stochastic processes which cover standard topics such as Poisson process, Brownian motion, renewal theory and random walks deal inadequately with their applications. Written in a simple and accessible manner, this book addresses that inadequacy and provides guidelines and tools to study the applications. The coverage includes research developments in Markov property, martingales, regenerative phenomena and Tauberian theorems, and covers measure theory at an elementary level.

Risk, Ruin and Survival

Ricardas Zitikis,Jiandong Ren,Kristina Sendova
Risk Ruin and Survival Book PDF

Author : Ricardas Zitikis,Jiandong Ren,Kristina Sendova
Publisher : MDPI
Page : 210 pages
File Size : 53,6 Mb
Release : 2020-04-02
Category : Business & Economics
ISBN : 9783039285167

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Risk, Ruin and Survival by Ricardas Zitikis,Jiandong Ren,Kristina Sendova Pdf

Developing techniques for assessing various risks and calculating probabilities of ruin and survival are exciting topics for mathematically-inclined academics. For practicing actuaries and financial engineers, the resulting insights have provided enormous opportunities but also created serious challenges to overcome, thus facilitating closer cooperation between industries and academic institutions. In this book, several renown researchers with extensive interdisciplinary research experiences share their thoughts that, in one way or another, contribute to the betterment of practice and theory of decision making under uncertainty. Behavioral, cultural, mathematical, and statistical aspects of risk assessment and modelling have been explored, and have been often illustrated using real and simulated data. Topics range from financial and insurance risks to security-type risks, from one-dimensional to multi- and even infinite-dimensional risks. The articles in the book were written with a broad audience in mind and should provide enjoyable reading for those with university level degrees and/or those who have studied for accreditation by various actuarial and financial societies.

Modeling Anomalous Diffusion: From Statistics To Mathematics

Weihua Deng,Ru Hou,Wanli Wang,Pengbo Xu
Modeling Anomalous Diffusion From Statistics To Mathematics Book PDF

Author : Weihua Deng,Ru Hou,Wanli Wang,Pengbo Xu
Publisher : World Scientific
Page : 267 pages
File Size : 44,8 Mb
Release : 2020-01-06
Category : Mathematics
ISBN : 9789811213014

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Modeling Anomalous Diffusion: From Statistics To Mathematics by Weihua Deng,Ru Hou,Wanli Wang,Pengbo Xu Pdf

This book focuses on modeling the anomalous diffusion phenomena, being ubiquitous in the natural world. Both the microscopic models (stochastic processes) and macroscopic models (partial differential equations) have been built up. The relationships between the two kinds of models are clarified, and based on these models, some statistical observables are analyzed. From statistics to mathematics, the built models show their power with their associated applications.This book is important for students to develop basic skills to be able to succeed in their future research. In addition to introducing the related models or methods, it also provides the corresponding applications and simulation results, which will attract more readers ranging from mathematicians to physicists or chemists, to name a few.

Stopped Random Walks

Allan Gut
Stopped Random Walks Book PDF

Author : Allan Gut
Publisher : Springer Science & Business Media
Page : 263 pages
File Size : 49,9 Mb
Release : 2009-04-03
Category : Mathematics
ISBN : 9780387878355

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Stopped Random Walks by Allan Gut Pdf

Classical probability theory provides information about random walks after a fixed number of steps. For applications, however, it is more natural to consider random walks evaluated after a random number of steps. Examples are sequential analysis, queuing theory, storage and inventory theory, insurance risk theory, reliability theory, and the theory of contours. Stopped Random Walks: Limit Theorems and Applications shows how this theory can be used to prove limit theorems for renewal counting processes, first passage time processes, and certain two-dimenstional random walks, and to how these results are useful in various applications. This second edition offers updated content and an outlook on further results, extensions and generalizations. A new chapter examines nonlinear renewal processes in order to present the analagous theory for perturbed random walks, modeled as a random walk plus "noise."