Probability Metrics And The Stability Of Stochastic Models
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Author | : Svetlozar T. Rachev |
Publisher | : |
Total Pages | : 520 |
Release | : 1991-05-13 |
Genre | : Mathematics |
ISBN | : |
Concentrates on four specialized research directions as well as applications to different problems of probability theory. These include: description of the basic structure of p. metrics, analysis of the topologies in the space of probability measures generated by different types of p. metrics, characterization of the ideal metrics for the given problem and investigations of the main relationships between different types of p. metrics. The presentation here is given in a general form, although specific cases are considered as they arise in the process of finding supplementary bounds or in applications to important special cases.
Author | : Alexander Zeifman |
Publisher | : MDPI |
Total Pages | : 370 |
Release | : 2021-03-05 |
Genre | : Mathematics |
ISBN | : 3036504524 |
The aim of this Special Issue of Mathematics is to commemorate the outstanding Russian mathematician Vladimir Zolotarev, whose 90th birthday will be celebrated on February 27th, 2021. The present Special Issue contains a collection of new papers by participants in sessions of the International Seminar on Stability Problems for Stochastic Models founded by Zolotarev. Along with research in probability distributions theory, limit theorems of probability theory, stochastic processes, mathematical statistics, and queuing theory, this collection contains papers dealing with applications of stochastic models in modeling of pension schemes, modeling of extreme precipitation, construction of statistical indicators of scientific publication importance, and other fields.
Author | : Svetlozar T. Rachev |
Publisher | : John Wiley & Sons |
Total Pages | : 264 |
Release | : 2011-03-10 |
Genre | : Business & Economics |
ISBN | : 1444392700 |
A Probability Metrics Approach to Financial Risk Measures relates the field of probability metrics and risk measures to one another and applies them to finance for the first time. Helps to answer the question: which risk measure is best for a given problem? Finds new relations between existing classes of risk measures Describes applications in finance and extends them where possible Presents the theory of probability metrics in a more accessible form which would be appropriate for non-specialists in the field Applications include optimal portfolio choice, risk theory, and numerical methods in finance Topics requiring more mathematical rigor and detail are included in technical appendices to chapters
Author | : Svetlozar Todorov Rachev |
Publisher | : |
Total Pages | : 508 |
Release | : 200? |
Genre | : Limit theorems (Probability theory) |
ISBN | : 9780608212883 |
Author | : S?ren Asmussen |
Publisher | : World Scientific |
Total Pages | : 621 |
Release | : 2010 |
Genre | : Mathematics |
ISBN | : 9814282529 |
The book gives a comprehensive treatment of the classical and modern ruin probability theory. Some of the topics are Lundberg's inequality, the Cramr?Lundberg approximation, exact solutions, other approximations (e.g., for heavy-tailed claim size distributions), finite horizon ruin probabilities, extensions of the classical compound Poisson model to allow for reserve-dependent premiums, Markov-modulation, periodicity, change of measure techniques, phase-type distributions as a computational vehicle and the connection to other applied probability areas, like queueing theory. In this substantially updated and extended second version, new topics include stochastic control, fluctuation theory for Levy processes, Gerber?Shiu functions and dependence.
Author | : V.V. Kalashnikov |
Publisher | : Springer |
Total Pages | : 317 |
Release | : 2006-11-14 |
Genre | : Mathematics |
ISBN | : 3540395989 |
Author | : Sean Meyn |
Publisher | : Cambridge University Press |
Total Pages | : 623 |
Release | : 2009-04-02 |
Genre | : Mathematics |
ISBN | : 0521731828 |
New up-to-date edition of this influential classic on Markov chains in general state spaces. Proofs are rigorous and concise, the range of applications is broad and knowledgeable, and key ideas are accessible to practitioners with limited mathematical background. New commentary by Sean Meyn, including updated references, reflects developments since 1996.
Author | : John M. Lachin |
Publisher | : John Wiley & Sons |
Total Pages | : 568 |
Release | : 2009-09-25 |
Genre | : Mathematics |
ISBN | : 0470317892 |
Comprehensive coverage of classical and modern methods of biostatistics Biostatistical Methods focuses on the assessment of risks and relative risks on the basis of clinical investigations. It develops basic concepts and derives biostatistical methods through both the application of classical mathematical statistical tools and more modern likelihood-based theories. The first half of the book presents methods for the analysis of single and multiple 2x2 tables for cross-sectional, prospective, and retrospective (case-control) sampling, with and without matching using fixed and two-stage random effects models. The text then moves on to present a more modern likelihood- or model-based approach, which includes unconditional and conditional logistic regression; the analysis of count data and the Poisson regression model; and the analysis of event time data, including the proportional hazards and multiplicative intensity models. The book contains a technical appendix that presents the core mathematical statistical theory used for the development of classical and modern statistical methods. Biostatistical Methods: The Assessment of Relative Risks: * Presents modern biostatistical methods that are generalizations of the classical methods discussed * Emphasizes derivations, not just cookbook methods * Provides copious reference citations for further reading * Includes extensive problem sets * Employs case studies to illustrate application of methods * Illustrates all methods using the Statistical Analysis System(r) (SAS) Supplemented with numerous graphs, charts, and tables as well as a Web site for larger data sets and exercises, Biostatistical Methods: The Assessment of Relative Risks is an excellent guide for graduate-level students in biostatistics and an invaluable reference for biostatisticians, applied statisticians, and epidemiologists.
Author | : Dirk Blomker |
Publisher | : World Scientific |
Total Pages | : 137 |
Release | : 2007-04-24 |
Genre | : Mathematics |
ISBN | : 9814475513 |
Rigorous error estimates for amplitude equations are well known for deterministic PDEs, and there is a large body of literature over the past two decades. However, there seems to be a lack of literature for stochastic equations, although the theory is being successfully used in the applied community, such as for convective instabilities, without reliable error estimates at hand. This book is the first step in closing this gap.The author provides details about the reduction of dynamics to more simpler equations via amplitude or modulation equations, which relies on the natural separation of time-scales present near a change of stability.For students, the book provides a lucid introduction to the subject highlighting the new tools necessary for stochastic equations, while serving as an excellent guide to recent research.
Author | : M.M. Rao |
Publisher | : CRC Press |
Total Pages | : 426 |
Release | : 1997-03-06 |
Genre | : Mathematics |
ISBN | : 9780849380785 |
Real and Stochastic Analysis: Recent Advances presents a carefully edited collection of research articles written by research mathematicians and highlighting advances in RSA. A balanced blend of both theory and applications, this book covers six aspects of stochastic analysis in depth and detail. The first chapters cover the state of the art in tracers analysis, stochastic modeling as it applies to AIDS epidemiology, and the current state of higher order SDEs. Subsequent chapters present a simple approach to Gaussian dichotomy, an overview of harmonizable processes, and stochastic Fubini and Green theorems. Common to all the chapters, the employment of functional analytic methods creates a unified approach. Each chapter includes detailed proofs. Throughout the book, a substantial amount of new material is presented, much of it for the first time. This forward-looking work presents current accounts of important areas of research, evaluates recent advances, and identifies research frontiers and new challenges.