Stochastic Programing

Stable Levy processes and related stochastic processes play an important role in stochastic modelling in applied sciences, in particular in financial mathematics. This book is about the potential theo

Dependence with complete connections is a more general type of stochastic process than the well-known Markovian dependence, accounting for a complete history of a stochastic evolution. This book is an authoritative survey of knowledge of the subject, dealing with the basic theoretical understanding and also with applications. These arise in a variety of situations as diverse as stochastic models of learning, branching processes in random environments, continued fractions and dynamical systems. Thus the book will appeal to mathematicians working in probability theory, ergodic theory and number theory, as well as applied mathematicians, engineers, biologists and social scientists interested in applications of stochastic methods.

Reliability and survival analysis are important applications of stochastic mathematics (probability, statistics and stochastic processes) that are usually covered separately in spite of the similarity

Over the last thirty years there has been extensive use of continuous time econometric methods in macroeconomic modelling. This monograph presents a continuous time macroeconometric model of the United Kingdom incorporating stochastic trends. Its development represents a major step forward in continuous time macroeconomic modelling. The book describes the model in detail and, like earlier models, it is designed in such a way as to permit a rigorous mathematical analysis of its steady-state and stability properties, thus providing a valuable check on the capacity of the model to generate plausible long-run behaviour. The model is estimated using newly developed exact Gaussian estimation methods for continuous time econometric models incorporating unobservable stochastic trends. The book also includes discussion of the application of the model to dynamic analysis and forecasting.

This book provides readers with an understanding of the fundamentals and applications of structural reliability, stochastic finite element method, reliability analysis via stochastic expansion, and op

This advanced engineering text describes methods developed to deal with stochastic aspects of structural behavior, providing a framework for evaluating, comparing, and combining stochastic effects. To

Stochastic differential equations (SDEs) are a powerful tool in science, mathematics, economics and finance. This book will help the reader to master the basic theory and learn some applications of SD

This book offers a systematic and comprehensive exposition of the quantum stochastic methods that have been developed in the field of quantum optics. It includes new treatments of photodetection, quan

This book offers a systematic and comprehensive exposition of the quantum stochastic methods that have been developed in the field of quantum optics. It includes new treatments of photodetection, quan

Stochastic approximation is a relatively new technique for studying the properties of an experimental situation; it has important applications in fields such as medicine and engineering. The subject can be treated either largely as a branch of pure mathematics, or else from an empirical and practical angle. In this book, Dr Wasan gives a rigorous mathematical treatment of the subject, drawing together the scattered results of a number of authors. He discusses the conditions under which the method gives a valid approximation to the required solution; methods for optimal choice of parameters to hasten convergence; the comparison of the method with other techniques. The discussion and proofs of theorems are given in enough detail to make them easy to follow, while a number of interesting examples show how the techniques may be applied in many fields.

The subject of the book is the comprehensive consideration of uncertainty in the numerical analysis, the safety assessment, and the design of structures. Stochastic as well as non-stochastic uncertain

A comprehensive overview of weak convergence of stochastic processes and its application to the study of financial markets. Split into three parts, the first recalls the mathematics of stochastic proc

In methodology, a two-equation generalized stochastic frontier model is used to study the dynamic and stochastic behavior of productive efficiency through time. The model represents an important exten

This book provides an accessible introduction to stochastic processes in physics and describes the basic mathematical tools of the trade: probability, random walks, and Wiener and Ornstein-Uhlenbeck p

This book provides a thorough and self-contained study of interdependence and complexity in settings of functional analysis, harmonic analysis and stochastic analysis. It focuses on 'dimension' as a basic counter of degrees of freedom, leading to precise relations between combinatorial measurements and various indices originating from the classical inequalities of Khintchin, Littlewood and Grothendieck. The basic concepts of fractional Cartesian products and combinatorial dimension are introduced and linked to scales calibrated by harmonic-analytic and stochastic measurements. Topics include the (two-dimensional) Grothendieck inequality and its extensions to higher dimensions, stochastic models of Brownian motion, degrees of randomness and Frechet measures in stochastic analysis. This book is primarily aimed at graduate students specialising in harmonic analysis, functional analysis or probability theory. It contains many exercises and is suitable to be used as a textbook. It is also o

Primarily an introduction to the theory of stochastic processes at the undergraduate or beginning graduate level, the primary objective of this book is to initiate students in the art of stochastic mo

The notion of 'stopping times' is a useful one in probability theory; it can be applied to both classical problems and fresh ones. This book presents this technique in the context of the directed set, stochastic processes indexed by directed sets, and many applications in probability, analysis and ergodic theory. Martingales and related processes are considered from several points of view. The book opens with a discussion of pointwise and stochastic convergence of processes, with concise proofs arising from the method of stochastic convergence. Later, the rewording of Vitali covering conditions in terms of stopping times clarifies connections with the theory of stochastic processes. Solutions are presented here for nearly all the open problems in the Krickeberg convergence theory for martingales and submartingales indexed by directed set. Another theme of the book is the unification of martingale and ergodic theorems.

This book is based on a course given at Massachusetts Institute of Technology. It is intended to be a reasonably self-contained introduction to stochastic analytic techniques that can be used in the study of certain problems. The central theme is the theory of diffusions. In order to emphasize the intuitive aspects of probabilistic techniques, diffusion theory is presented as a natural generalization of the flow generated by a vector field. Essential to the development of this idea is the introduction of martingales and the formulation of diffusion theory in terms of martingales. The book will make valuable reading for advanced students in probability theory and analysis and will be welcomed as a concise account of the subject by research workers in these fields.

This textbook introduces readers to the fundamental notions of modern probability theory. The only prerequisite is a working knowledge in real analysis. Highlighting the connections between martingales and Markov chains on one hand, and Brownian motion and harmonic functions on the other, this book provides an introduction to the rich interplay between probability and other areas of analysis.Arranged into three parts, the book begins with a rigorous treatment of measure theory, with applications to probability in mind. The second part of the book focuses on the basic concepts of probability theory such as random variables, independence, conditional expectation, and the different types of convergence of random variables. In the third part, in which all chapters can be read independently, the reader will encounter three important classes of stochastic processes: discrete-time martingales, countable state-space Markov chains, and Brownian motion. Each chapter ends with a selection of illu

The theoretical aspects of the book are based on an essential introduction to the building blocks of the two topics under consideration: mathematical programming and stochastic processes. It also 

The theoretical aspects of the book are based on an essential introduction to the building blocks of the two topics under consideration: mathematical programming and stochastic processes. It also 

Rigorous mathematical finance relies strongly on two additional fields: optimal stopping and stochastic analysis. This book is the first one which presents not only main results in the mathematical fi

This book focuses on modeling the anomalous diffusion phenomena, being ubiquitous in the natural world. Both the microscopic models (stochastic processes) and macroscopic models (partial differential

Noisy optimization is a topic of growing interest for researchers working on mainstream optimization problems. Although several techniques for dealing with stochastic noise in optimization problems ar

Drawing on advanced probability theory, Ambit Stochastics is used to model stochastic processes which depend on both time and space. This monograph, the first on the subject, provides a reference for

This textbook offers a compact introductory course on Malliavin calculus, an active and powerful area of research. It covers recent applications, including density formulas, regularity of probability laws, central and non-central limit theorems for Gaussian functionals, convergence of densities and non-central limit theorems for the local time of Brownian motion. The book also includes a self-contained presentation of Brownian motion and stochastic calculus, as well as Lévy processes and stochastic calculus for jump processes. Accessible to non-experts, the book can be used by graduate students and researchers to develop their mastery of the core techniques necessary for further study.

This textbook offers a compact introductory course on Malliavin calculus, an active and powerful area of research. It covers recent applications, including density formulas, regularity of probability laws, central and non-central limit theorems for Gaussian functionals, convergence of densities and non-central limit theorems for the local time of Brownian motion. The book also includes a self-contained presentation of Brownian motion and stochastic calculus, as well as Lévy processes and stochastic calculus for jump processes. Accessible to non-experts, the book can be used by graduate students and researchers to develop their mastery of the core techniques necessary for further study.

This book presents the latest developments and breakthroughs in fuzzy theory and performance prediction of queuing and reliability models by using the stochastic modeling and optimization theory. The

This 49th volume offers a good sample of the main streams of current research on probability and stochastic processes, in particular those active in France. This includes articles on latest developmen

Piecewise-deterministic Markov processes form a class of stochastic models with a sizeable scope of applications: biology, insurance, neuroscience, networks, finance... Such processes are defined by a

This book focuses on statistical inferences related to various combinatorial stochastic processes. Specifically, it discusses the intersection of three subjects that are generally studied independentl

Refection Positivity is a central theme at the crossroads of Lie group representations, euclidean and abstract harmonic analysis, constructive quantum field theory, and stochastic processes.This book

This book covers various modern theoretical, technical, practical and technological aspects of computerized numerical control and control systems of deterministic and stochastic dynamical processes.

The purpose of this book is twofold: first, it sets out to equip the reader with a sound understanding of the foundations of probability theory and stochastic processes, offering step-by-step guidance

This book provides a comprehensive presentation of classical and advanced topics in estimation and control of dynamical systems with an emphasis on stochastic control. Many aspects which are not

This monograph deals primarily with the prediction of vector valued stochastic processes that are either weakly stationary, or have weakly stationary increments, from finite segments of their past. Th

This is a monograph on the emerging branch of mathematical biophysics combining asymptotic analysis with numerical and stochastic methods to analyze partial differential equations arising in biologica

This book provides new theories, applications and quantitative methods in demography, population studies and statistics. It presents and applies data analysis, statistics and stochastic modeling techn

This book focuses on maximum principle and verification theorem for incomplete information forward-backward stochastic differential equations (FBSDEs) and their applications in linear-quadratic optima

Economic forecasting is a key ingredient of decision making both in the public and in the private sector. Because economic outcomes are the result of a vast, complex, dynamic and stochastic system, fo