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.

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.

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.

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.

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

This third volume presents further equivalents to the Riemann hypothesis and explores its decidability.

This book communicates some contemporary mathematical and statistical developments in river basin hydrology as they pertain to space-time rainfall, spatial landform and network structures and their role in understanding averages and fluctuations in the hydrologic water balance of river basins. While many of the mathematical and statistical nations have quite classical mathematical roots, the river basin data structure has led to many variations on the problems and theory.

Probability and Statistics theme is a component of Encyclopedia of Mathematical Sciences in the global Encyclopedia of Life Support Systems (EOLSS), which is an integrated compendium of twenty one Encyclopedias. The Theme with contributions from distinguished experts in the field, discusses Probability and Statistics. Probability is a standard mathematical concept to describe stochastic uncertainty. Probability and Statistics can be considered as the two sides of a coin. They consist of methods for modeling uncertainty and measuring real phenomena. Today many important political, health, and economic decisions are based on statistics. This theme is structured in five main topics: Probability and Statistics; Probability Theory; Stochastic Processes and Random Fields; Probabilistic Models and Methods; Foundations of Statistics, which are then expanded into multiple subtopics, each as a chapter. These three volumes are aimed at the following five major target audiences: University and College students Educators, Professional practitioners, Research personnel and Policy analysts, managers, and decision makers and NGOs.

This monograph is a gateway for researchers and graduate students to explore the profound, yet subtle, world of long-range dependence (also known as long memory). The text is organized around the probabilistic properties of stationary processes that are important for determining the presence or absence of long memory. The first few chapters serve as an overview of the general theory of stochastic processes which gives the reader sufficient background, language, and models for the subsequent discussion of long memory. The later chapters devoted to long memory begin with an introduction to the subject along with a brief history of its development, followed by a presentation of what is currently the best known approach, applicable to stationary processes with a finite second moment. The book concludes with a chapter devoted to the author’s own, less standard, point of view of long memory as a phase transition, and even includes some novel results. Most of the material in the book has not previously been published in a single self-contained volume, and can be used for a one- or two-semester graduate topics course. It is complete with helpful exercises and an appendix which describes a number of notions and results belonging to the topics used frequently throughout the book, such as topological groups and an overview of the Karamata theorems on regularly varying functions.