Level Crossing Problems And Inverse Gaussian Distributions
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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 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, 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 theoretical background in level-crossing problem, e.g., from the insurance industry, can 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
Level-Crossing Problems and Inverse Gaussian Distributions by Vsevolod K. Malinovskii Pdf
Primarily aimed at researchers and postgraduates, but may be of interest to some professionals working in related fields, such as the insurance industry Suitable as supplementary reading for a standard course in applied probability Requires minimal prerequisites in mathematical analysis and probability theory
Risk Measures and Insurance Solvency Benchmarks by Vsevolod K. Malinovskii Pdf
Risk Measures and Insurance Solvency Benchmarks: Fixed-Probability Levels in Renewal Risk Models is written for academics and practitioners who are concerned about potential weaknesses of the Solvency II regulatory system. It is also intended for readers who are interested in pure and applied probability, have a taste for classical and asymptotic analysis, and are motivated to delve into rather intensive calculations. The formal prerequisite for this book is a good background in analysis. The desired prerequisite is some degree of probability training, but someone with knowledge of the classical real-variable theory, including asymptotic methods, will also find this book interesting. For those who find the proofs too complicated, it may be reassuring that most results in this book are formulated in rather elementary terms. This book can also be used as reading material for basic courses in risk measures, insurance mathematics, and applied probability. The material of this book was partly used by the author for his courses in several universities in Moscow, Copenhagen University, and in the University of Montreal. Features Requires only minimal mathematical prerequisites in analysis and probability Suitable for researchers and postgraduate students in related fields Could be used as a supplement to courses in risk measures, insurance mathematics and applied probability.
Communications and Networks by Ian F. Blake,H. Vincent Poor Pdf
The areas of communications, computer networks, and signal processing have undergone rapid development over the past several years. The advent of VLSI circuitry and increasingly sophisticated computer hardware and software techniques have made possible the construction of systems and signal proces sors for· communications applications not contemplated only a short time ago. The increasing complexity of communication systems, both by themselves and in land-based or satellite networks, has created a greater need for finding use ful mathematical techniques for their analysis. The rapidly evolving technolo gies involved continue to find exciting new areas for application, and it remains a challenge for researchers to keep abreast of developments. In this volume researchers from a broad cross section of the areas of communications, signal processing, and computer networks have been invited to contribute articles to assist readers in learning about the current state of research and future research directions in their area. The authors were not given tight guidelines for their contributions and thus the character and emphasis of each chapter differs. Although the scope of the areas considered is necessarily limited in a volume of this size, the coverage here is quite broad and it is hoped that the reader will find the contents of this volume to be interesting, useful, and informative.
The Center and Focus Problem by M.N. Popa,V.V. Pricop Pdf
The Center and Focus Problem: Algebraic Solutions and Hypotheses, M. N. Popa and V.V. Pricop, ISBN: 978-1-032-01725-9 (Hardback) This book focuses on an old problem of the qualitative theory of differential equations, called the Center and Focus Problem. It is intended for mathematicians, researchers, professors and Ph.D. students working in the field of differential equations, as well as other specialists who are interested in the theory of Lie algebras, commutative graded algebras, the theory of generating functions and Hilbert series. The book reflects the results obtained by the authors in the last decades. A rather essential result is obtained in solving Poincaré's problem. Namely, there are given the upper estimations of the number of Poincaré-Lyapunov quantities, which are algebraically independent and participate in solving the Center and Focus Problem that have not been known so far. These estimations are equal to Krull dimensions of Sibirsky graded algebras of comitants and invariants of systems of differential equations. Table of Contents 1. Lie Algebra Of Operators Of Centro-Affine Group Representation In The Coefficient Space Of Polynomial Differential Systems 2. Differential Equations For Centro-Affine Invariants And Comitants Of Differential Systems And Their Applications 3. Generating Functions And Hilbert Series For Sibirsky Graded Algebras Of Comitants And Invariants Of Differential Systems 4. Hilbert Series For Sibirsky Algebras And Krull Dimension For Them 5. About The Center And Focus Problem 6. On The Upper Bound Of The Number Of Algebraically Independent Focus Quantities That Take Part In Solving The Center And Focus Problem For The System s(1,m1,...,m`) 7. On The Upper Bound Of The Number Of Algebraically Independent Focus Quantities That Take Part In Solving The Center And Focus Problem For Lyapunov System. Bibliography Appendixes Biographies Popa Mihail Nicolae, holds a Ph.D. from Gorky University (now Nizhny Novgorod, Russia). He has served as Director and Deputy Director of Vladimir Andrunachievici Institute of Mathematics and Computer Science (IMCS)) in the Laboratory of Differential Equations. He is Professor at the State University of Tiraspol (based in Chisinau). His scientific interests are related to the invariant processes in the qualitative theory of differential equations, Lie algebras and commutative graded algebras, generating functions and Hilbert series, orbit theory, Lyapunov stability theory. Pricop Victor Vasile, holds a Ph.D. from Vladimir Andrunachievici Institute of Mathematics and Computer Science. He is professor at the State Institute of International Relations of Moldova. Victor Pricop's scientific interests are related to Lie algebras and graded algebras of invariants and comitants, generating functions and Hilbert series, applications of algebras to polynomial differential systems.
Abstract Calculus by Francisco Javier Garcia-Pacheco Pdf
Abstract Calculus: A Categorical Approach provides an abstract approach to calculus. It is intended for graduate students pursuing PhDs in pure mathematics but junior and senior researchers in basically any field of mathematics and theoretical physics will also be interested. Any calculus text for undergraduate students majoring in engineering, mathematics or physics deals with the classical concepts of limits, continuity, differentiability, optimization, integrability, summability, and approximation. This book covers the exact same topics, but from a categorical perspective, making the classification of topological modules as the main category involved. Features Suitable for PhD candidates and researchers Requires prerequisites in set theory, general topology, and abstract algebra, but is otherwise self-contained Dr. Francisco Javier García-Pacheco is a full professor and Director of the Departmental Section of Mathematics at the College of Engineering of the University of Cádiz, Spain.
Noncommutative Polynomial Algebras of Solvable Type and Their Modules by Huishi Li Pdf
Noncommutative Polynomial Algebras of Solvable Type and Their Modules is the first book to systematically introduce the basic constructive-computational theory and methods developed for investigating solvable polynomial algebras and their modules. In doing so, this book covers: A constructive introduction to solvable polynomial algebras and Gröbner basis theory for left ideals of solvable polynomial algebras and submodules of free modules The new filtered-graded techniques combined with the determination of the existence of graded monomial orderings The elimination theory and methods (for left ideals and submodules of free modules) combining the Gröbner basis techniques with the use of Gelfand-Kirillov dimension, and the construction of different kinds of elimination orderings The computational construction of finite free resolutions (including computation of syzygies, construction of different kinds of finite minimal free resolutions based on computation of different kinds of minimal generating sets), etc. This book is perfectly suited to researchers and postgraduates researching noncommutative computational algebra and would also be an ideal resource for teaching an advanced lecture course.
Fixed Point Results in W-Distance Spaces by Vladimir Rakočević Pdf
Fixed Point Results in W-Distance Spaces is a self-contained and comprehensive reference for advanced fixed-point theory and can serve as a useful guide for related research. The book can be used as a teaching resource for advanced courses on fixed-point theory, which is a modern and important field in mathematics. It would be especially valuable for graduate and postgraduate courses and seminars. Features Written in a concise and fluent style, covers a broad range of topics and includes related topics from research. Suitable for researchers and postgraduates. Contains brand new results not published elsewhere.
Insurance Planning Models: Price Competition And Regulation Of Financial Stability by Vsevolod Malinovskii Pdf
Insurance Planning Models: Price Competition and Regulation of Financial Stability is an exciting new book that takes readers inside the secrets of internal organization of the modern general insurance business. Many people know that it is subject to intensive state regulation, whereby the purpose is to maintain long-term efficiency, honesty, security and stability in the interest and for the protection of policyholders. However, except for knowing that the insurance system is regulated by intensive calculations, that the insurance companies have different positions on the market, that they pursue different goals and even compete with each other, and that one of the tools of this competition is the policy price, not so many people know how to achieve these deserving goals.In developing quantitative recommendations and directives to competing insurers, regulators rely on certain models. In the 1900s, such models were proposed. They were useful for an insight into the probabilistic nature of the insurance process, but not for direct application to practically meaningful problems of insurance regulation. This book is your guide to the rigorously constructed long-term dynamic models with the aim to improve regulatory methods and develop quantitative recommendations using both analytical calculations and computer simulation. It is addressed to a wide range of readers, including interested policyholders, economists whose interest lies in insurance management and regulation, and mathematicians wishing to expand the scope of application for their knowledge.This book is devoted to certain issues that are either not sufficiently presented, or even absent in the literature. It is an attempt to penetrate from the standpoint of mathematical modeling into the goals which face insurance regulators and contending company managers for preventing insolvencies, or even crises pertinent to badly regulated complex reflexive systems.It offers rigorous probabilistic models of long-term insurance business based on the laws of mass phenomena. They mitigate deficiencies of oversimplified risk models. The book presents advances in probabilistic techniques designed to seek quantitative, rather than qualitative, directives and recommendations regarding safe control aiming to achieve different business goals.
The Inverse Gaussian Distribution by Raj Chhikara Pdf
This monograph is a compilation of research on the inverse Gaussian distribution. It emphasizes the presentation of the statistical properties, methods, and applications of the two-parameter inverse Gaussian family of distribution. It is useful to statisticians and users of statistical distribution.
An Author and Permuted Title Index to Selected Statistical Journals by Brian L. Joiner Pdf
All articles, notes, queries, corrigenda, and obituaries appearing in the following journals during the indicated years are indexed: Annals of mathematical statistics, 1961-1969; Biometrics, 1965-1969#3; Biometrics, 1951-1969; Journal of the American Statistical Association, 1956-1969; Journal of the Royal Statistical Society, Series B, 1954-1969,#2; South African statistical journal, 1967-1969,#2; Technometrics, 1959-1969.--p.iv.
Current Advances in Mechanical Design and Production VII by M.F. Hassan,S.M. Megahed Pdf
The International Conference on Mechanical Design and Production has over the years established itself as an excellent forum for the exchange of ideas in these established fields. The first of these conferences was held in 1979. The seventh, and most recent, conference in the series was held in Cairo during February 15-17, 2000. International engineers and scientists gathered to exchange experiences and highlight the state-of-the-art research in the fields of mechanical design and production. In addition a heavy emphasis was placed on the issue of technology transfer. Over 100 papers were accepted for presentation at the conference. Current Advances in Mechanical Design & Production VII does not, however, attempt to publish the complete work presented but instead offers a sample that represents the quality and breadth of both the work and the conference. Ten invited papers and 54 ordinary papers have been selected for inclusion in these proceedings. They cover a range of basic and applied topics that can be classified into six main categories: System Dynamics, Solid Mechanics, Material Science, Manufacturing Processes, Design and Tribology, and Industrial Engineering and its Applications.
Stochastic Reliability and Maintenance Modeling by Tadashi Dohi,Toshio Nakagawa Pdf
In honor of the work of Professor Shunji Osaki, Stochastic Reliability and Maintenance Modeling provides a comprehensive study of the legacy of and ongoing research in stochastic reliability and maintenance modeling. Including associated application areas such as dependable computing, performance evaluation, software engineering, communication engineering, distinguished researchers review and build on the contributions over the last four decades by Professor Shunji Osaki. Fundamental yet significant research results are presented and discussed clearly alongside new ideas and topics on stochastic reliability and maintenance modeling to inspire future research. Across 15 chapters readers gain the knowledge and understanding to apply reliability and maintenance theory to computer and communication systems. Stochastic Reliability and Maintenance Modeling is ideal for graduate students and researchers in reliability engineering, and workers, managers and engineers engaged in computer, maintenance and management works.