Structured Dependence Between Stochastic Processes
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| Author | : Tomasz R. Bielecki |
| Publisher | : Cambridge University Press |
| Total Pages | : 280 |
| Release | : 2020-08-27 |
| Genre | : Mathematics |
| ISBN | : 1108895379 |
The relatively young theory of structured dependence between stochastic processes has many real-life applications in areas including finance, insurance, seismology, neuroscience, and genetics. With this monograph, the first to be devoted to the modeling of structured dependence between random processes, the authors not only meet the demand for a solid theoretical account but also develop a stochastic processes counterpart of the classical copula theory that exists for finite-dimensional random variables. Presenting both the technical aspects and the applications of the theory, this is a valuable reference for researchers and practitioners in the field, as well as for graduate students in pure and applied mathematics programs. Numerous theoretical examples are included, alongside examples of both current and potential applications, aimed at helping those who need to model structured dependence between dynamic random phenomena.
| Author | : Youssef Elouerkhaoui |
| Publisher | : Springer |
| Total Pages | : 466 |
| Release | : 2017-11-15 |
| Genre | : Business & Economics |
| ISBN | : 3319609734 |
This book provides an advanced guide to correlation modelling for credit portfolios, providing both theoretical underpinnings and practical implementation guidance. The book picks up where pre-crisis credit books left off, offering guidance for quants on the latest tools and techniques for credit portfolio modelling in the presence of CVA (Credit Value Adjustments). Written at an advanced level, it assumes that readers are familiar with the fundamentals of credit modelling covered, for example, in the market leading books by Schonbucher (2003) and O’Kane (2008). Coverage will include the latest default correlation approaches; correlation modelling in the ‘Marshall-Olkin’ contagion framework, in the context of CVA; numerical implementation; and pricing, calibration and risk challenges. The explosive growth of credit derivatives markets in the early-to-mid 000’s was bought to a close by the 2007 financial crisis, where these instruments were held largely to blame for the economic downturn. However, in the wake of increased regulation across all financial instruments and the challenge of buying and selling bonds in large amounts, credit derivatives have once again been found to be the answer and the market has grown significantly. Written by a practitioner for practitioners, this book will also interest researchers in mathematical finance who want to understand how things happen and work ‘on the floor’. Building the reader’s knowledge from the ground up, and with numerous real life examples used throughout, this book will prove a popular reference for anyone with a mathematical mind interested credit markets.
| Author | : Volker Schmitz |
| Publisher | : |
| Total Pages | : 110 |
| Release | : 2003 |
| Genre | : |
| ISBN | : 9783832212780 |
| Author | : Roderick Melnik |
| Publisher | : Springer |
| Total Pages | : 437 |
| Release | : 2017-09-05 |
| Genre | : Mathematics |
| ISBN | : 1493969692 |
This volume is an excellent resource for professionals in various areas of applications of mathematics, modeling, and computational science. It focuses on recent progress and modern challenges in these areas. The volume provides a balance between fundamental theoretical and applied developments, emphasizing the interdisciplinary nature of modern trends and detailing state-of-the-art achievements in Applied Mathematics, Modeling, and Computational Science. The chapters have been authored by international experts in their respective fields, making this book ideal for researchers in academia, practitioners, and graduate students. It can also serve as a reference in the diverse selected areas of applied mathematics, modelling, and computational sciences, and is ideal for interdisciplinary collaborations.
| Author | : Victor Yu Korolev |
| Publisher | : Walter de Gruyter |
| Total Pages | : 424 |
| Release | : 2006 |
| Genre | : Plasma turbulence |
| ISBN | : 9789067644495 |
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 | : Uwe Küchler |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 325 |
| Release | : 2006-05-09 |
| Genre | : Mathematics |
| ISBN | : 0387227652 |
A comprehensive account of the statistical theory of exponential families of stochastic processes. The book reviews the progress in the field made over the last ten years or so by the authors - two of the leading experts in the field - and several other researchers. The theory is applied to a broad spectrum of examples, covering a large number of frequently applied stochastic process models with discrete as well as continuous time. To make the reading even easier for statisticians with only a basic background in the theory of stochastic process, the first part of the book is based on classical theory of stochastic processes only, while stochastic calculus is used later. Most of the concepts and tools from stochastic calculus needed when working with inference for stochastic processes are introduced and explained without proof in an appendix. This appendix can also be used independently as an introduction to stochastic calculus for statisticians. Numerous exercises are also included.
| Author | : Wolfgang Lay |
| Publisher | : Cambridge University Press |
| Total Pages | : 316 |
| Release | : 2024-05-23 |
| Genre | : Mathematics |
| ISBN | : 1009546589 |
Higher special functions emerge from boundary eigenvalue problems of Fuchsian differential equations with more than three singularities. This detailed reference provides solutions for singular boundary eigenvalue problems of linear ordinary differential equations of second order, exploring previously unknown methods for finding higher special functions. Starting from the fact that it is the singularities of a differential equation that determine the local, as well as the global, behaviour of its solutions, the author develops methods that are both new and efficient and lead to functional relationships that were previously unknown. All the developments discussed are placed within their historical context, allowing the reader to trace the roots of the theory back through the work of many generations of great mathematicians. Particular attention is given to the work of George Cecil Jaffé, who laid the foundation with the calculation of the quantum mechanical energy levels of the hydrogen molecule ion.
| Author | : Chun-Qing Li |
| Publisher | : Elsevier |
| Total Pages | : 626 |
| Release | : 2022-10-23 |
| Genre | : Technology & Engineering |
| ISBN | : 0323860168 |
Time-Dependent Reliability Theory and Its Applications introduces the theory of time-dependent reliability and presents methods to determine the reliability of structures over the lifespan of their services. The book contains state-of-the-art solutions to first passage probability derived from the theory of stochastic processes with different types of probability distribution functions, including Gaussian and non-Gaussian distributions and stationary and non-stationary processes. In addition, it provides various methods to determine the probability of failure over time, considering different failure modes and a methodology to predict the service life of structures. Sections also cover the applications of time-dependent reliability to prediction of service life and development of risk cost-optimized maintenance strategy for existing structures. This new book is for those who wants to know how to predict the service life of a structure (buildings, bridges, aircraft structures, etc.) and how to develop a risk-cost, optimized maintenance strategy for these structures. - Presents the basic knowledge required to predict service life and develop a maintenance strategy for infrastructure - Explains how to predict the remaining safe life of the infrastructure during its lifespan of operation - Describes how to carry out maintenance for an infrastructure to ensure its safe and serviceable operation during the designed service life
| Author | : Kevin Broughan |
| Publisher | : Cambridge University Press |
| Total Pages | : 705 |
| Release | : 2023-09-30 |
| Genre | : Mathematics |
| ISBN | : 1009384805 |
This third volume presents further equivalents to the Riemann hypothesis and explores its decidability.
| Author | : Kevin Broughan |
| Publisher | : Cambridge University Press |
| Total Pages | : 706 |
| Release | : 2023-09-30 |
| Genre | : Mathematics |
| ISBN | : 1009384775 |
This three-volume work presents the main known equivalents to the Riemann hypothesis, perhaps the most important problem in mathematics. Volume 3 covers new arithmetic and analytic equivalences from numerous studies in the field, such as Rogers and Tao, and presents derivations which show whether the Riemann hypothesis is decidable.
