Probability and statistics Books

The management of operational risk in the banking industry has undergone explosive changes over the last decade due to substantial changes in the operational environment. Globalization, deregulation, the use of complex financial products, and changes in...

Promptly growing demand for telecommunication services and information interchange has led to the fact that communication became one of the most dynamical branches of an infrastructure of a modern society.The book introduces to the bases of classical MDP...

Stochastic Analysis aims to provide mathematical tools to describe and model high dimensional random systems. Such tools arise in the study of Stochastic Differential Equations and Stochastic Partial Differential Equations, Infinite Dimensional...

Most financial and investment decisions are based on considerations of possible future changes and require forecasts on the evolution of the financial world. Time series and processes are the natural tools for describing the dynamic behavior of financial...

Community structure is a salient structural characteristic of many real-world networks. Communities are generally hierarchical, overlapping, multi-scale and coexist with other types of structural regularities of networks. This...

This book provides an example of a thorough statistical treatment of ocean wave data in space and time. It demonstrates how the flexible framework of Bayesian hierarchical space-time models can be applied to oceanographic processes such as significant...

The present volume contains the most advanced theories on the martingale approach to central limit theorems. Using the time symmetry properties of the Markov processes, the book develops the techniques that allow us to deal with infinite dimensional...

​In order to precisely model real-life systems or man-made devices, both nonlinear and dynamic properties need to be taken into account. The generic, black-box model based on Volterra and Wiener series is capable of representing fairly complicated...

The thesis deals with averaging dynamics in a multiagent networked system, which is a main mechanism for diffusing the information over such networks. It arises in a wide range of applications in engineered physical networks (such as mobile communication...

As usual, some of the contributions to this 44th Séminaire de Probabilités were presented during the Journées de Probabilités held in Dijon in June 2010. The remainder were spontaneous submissions or were solicited by the editors. The traditional and...

Selected papers submitted by participants of the international Conference "Stochastic Analysis and Applied Probability 2010" ( www.saap2010.org ) make up the basis of this volume.The SAAP 2010 was held in Tunisia, from 7-9 October, 2010, and was...

Since the publication of the first edition of the present volume in 1980, the stochastic stability of differential equations has become a very popular subject of research in mathematics and engineering. To date exact formulas for the Lyapunov exponent,...

Biological and other natural processes have always been a source of inspiration for computer science and information technology. Many emerging problem solving techniques integrate advanced evolution and cooperation strategies, encompassing a range of...

1 Introduction.- 2 Interest Rates and Related Contracts.- 2.1 Zero-Coupon Bonds.- 2.2 Interest Rates.- 2.2.1 Market Example: LIBOR.- 2.2.2 Simple vs. Continuous Compounding.- 2.2.3 Forward vs. Future Rates.- 2.3 Bank Account and Short Rates.- 2.4 Coupon...

In applications, and especially in mathematical finance, random time-dependent events are often modeled as stochastic processes. Assumptions are made about the structure of such processes, and serious researchers will want to justify those assumptions...

The main idea of statistical convergence is to demand convergence only for a majority of elements of a sequence. This method of convergence has been investigated in many fundamental areas of mathematics such as: measure theory, approximation theory,...

Measure-valued branching processes arise as high density limits of branching particle systems. The Dawson-Watanabe superprocess is a special class of those. The author constructs superprocesses with Borel right underlying motions and general branching...

This is a new, completely revised, updated and enlarged edition of the author's Ergebnisse vol. 46: "Spin Glasses: A Challenge for Mathematicians". This new edition will appear in two volumes, the present first volume presents the basic results and...

Methodology.- Modelling Framework.- Simulation Models.- Valuation and Sensitivities.- Architecture and Implementation.- Computational Framework.- Implementation.- Architecture.- Products.- Interest-Rate Products.- Equity, Commodity, Inflation and FX...

Discovery of Intrinsic Clustering in Spatial Data.- Statistical Approach to the Identification of Separation Surface for Spatial Data.- Algorithmic Approach to the Identification of Classification Rules or Separation Surface for Spatial Data.- Discovery...

Borel Sets, Measures and All That.- Modal Logics.- The Giry Monad: Randomized Morphisms.- Coalgebraic Logic.

The Paris-Princeton Lectures in Financial Mathematics, of which this is the fourth volume, publish cutting-edge research in self-contained, expository articles from outstanding specialists - established or on the rise! The aim is to produce a series of...

Over the past 10-15 years, we have seen a revival of general Levy ´ processes theory as well as a burst of new applications. In the past, Brownian motion or the Poisson process have been considered as appropriate models for...

Permutation and bootstrap statistics under infinite variance.- Max-Stable Processes: Representations, Ergodic Properties and Statistical Applications.- Best attainable rates of convergence for the estimation of the memory parameter.- Harmonic analysis...

After the ?rst edition of this book was published in early 2005, the world has changed dramatically and at a pace never seen before. The changes that - curred in 2008 and 2009 were completely unthinkable two years before. These changes took place not...

Copulas are mathematical objects that fully capture the dependence structure among random variables and hence offer great flexibility in building multivariate stochastic models. Since their introduction in the early 50's, copulas have gained considerable...

In financial and actuarial modeling and other areas of application, stochastic differential equations with jumps have been employed to describe the dynamics of various state variables. The numerical solution of such equations...

Early in my career I was given the task of designing a sub-critical nuclear reactor facility that was to be used to perform basic research in the area of reactor physics. We planned to run a series of experiments to determine fundamental parameters...

When I wrote the book Quantitative Sociodynamics, it was an early attempt to make methods from statistical physics and complex systems theory fruitful for the modeling and understanding of social phenomena. Unfortunately, the ?rst edition appeared at a...

Since Charles Spearman published his seminal paper on factor analysis in 1904 and Karl Joresk ¨ og replaced the observed variables in an econometric structural equation model by latent factors in 1970, causal modelling by means of latent variables has...

Il est souvent nécessaire de réaliser des expériences afin de modéliser le comportement d'un phénomène complexe. La méthode des plans d'expérience a pour objectif d'obtenir un maximum d'information sur le phénomène étudié en un minimum d'expériences...

Models.- The Poisson-Dirichlet Distribution.- The Two-Parameter Poisson-Dirichlet Distribution.- The Coalescent.- Stochastic Dynamics.- Particle Representation.- Asymptotic Behaviors.- Fluctuation Theorems.- Large Deviations for the Poisson-Dirichlet...

One of the charms of mathematics is the contrast between its generality and its applicability to concrete, even everyday, problems. Branching processes are typical in this. Their niche of mathematics is the abstract pattern of reproduction, sets of...

Seasonal patterns have been found in a remarkable range of health conditions, including birth defects, respiratory infections and cardiovascular disease. Accurately estimating the size and timing of seasonal peaks in disease incidence is an aid to...

Discovered in the seventies, Black-Scholes formula continues to play a central role in Mathematical Finance. We recall this formula. Let (B ,t? 0; F ,t? 0, P) - t t note a standard Brownian motion with B = 0, (F ,t? 0) being its natural ?ltra- 0 t t tion...

The Algebraic Framework of Unit-Root Econometrics.- The Statistical Setting.- Econometric Dynamic Models: From Classical Econometrics to Time Series Econometrics.

Independent Random Variables.- Classical Limit Theorems, Inequalities and Other Tools.- Self-Normalized Large Deviations.- Weak Convergence of Self-Normalized Sums.- Stein's Method and Self-Normalized Berry-Esseen Inequality.- Self-Normalized Moderate...

Foundations of Stochastic Geometry.- Prolog.- Random Closed Sets.- Point Processes.- Geometric Models.- Integral Geometry.- Averaging with Invariant Measures.- Extended Concepts of Integral Geometry.- Integral Geometric Transformations.- Selected Topics...

Modeling.- A Unified Description for Stochastic Discrete Event Systems.- Stochastic Timed Automata.- Queuing Models.- Simple Petri Nets.- Colored Petri Nets.- Evaluation.- Standard Quantitative Evaluation Methods for SDES.- An Iterative Approximation...

Prerequisites.- Probability Theory.- Credibility Theory.- Chance Theory.- Uncertainty Theory.- Supplements.

This unique book on the subject addresses fundamental problems and will be the standard reference for a long time to come. The authors have different scientific origins and combine these successfully, creating a text aimed at...

A treatment of estimating unknown parameters, testing hypotheses and estimating confidence intervals in linear models. Readers will find here presentations of the Gauss-Markoff model, the analysis of variance, the multivariate...

Leave nothing to chance. This cliche embodies the common belief that ran­ domness has no place in carefully planned methodologies, every step should be spelled out, each i dotted and each t crossed. In discrete mathematics at...

"This is a magnificent book! Its purpose is to describe in considerable detail a variety of techniques used by probabilists in the investigation of problems concerning Brownian motion....This is THE book for a capable graduate...

Part I. Probability. Basic Notions, Structure, Methods. Chapter 1: Introduction.- Chapter 2: The Probability Space.- Chapter 3: Independence.- Chapter 4. General Theory of Stochastic Processes and Random Functions.- Chapter 5. Limit Theorems.- Part II...

The numerical analysis of stochastic differential equations (SDEs) differs significantly from that of ordinary differential equations. This book provides an easily accessible introduction to SDEs, their applications and the...

This EMS volume provides an exposition of the structure theory of Fano varieties, i.e. algebraic varieties with an ample anticanonical divisor. This book will be very useful as a reference and research guide for researchers and...