Stochastic Programing

The vector-borne Zika virus joins avian influenza, Ebola, and yellow fever as recent public health crises threatening pandemicity.By a combination of stochastic modeling and economic geography, this b

Wick ordering of creation and annihilation operators is of fundamental importance for computing averages and correlations in quantum field theory and, by extension, in the Hudson–Parthasarathy theory of quantum stochastic processes, quantum mechanics, stochastic processes, and probability. This book develops the unified combinatorial framework behind these examples, starting with the simplest mathematically, and working up to the Fock space setting for quantum fields. Emphasizing ideas from combinatorics such as the role of lattice of partitions for multiple stochastic integrals by Wallstrom–Rota and combinatorial species by Joyal, it presents insights coming from quantum probability. It also introduces a 'field calculus' which acts as a succinct alternative to standard Feynman diagrams and formulates quantum field theory (cumulant moments, Dyson–Schwinger equation, tree expansions, 1-particle irreducibility) in this language. Featuring many worked examples, the book is aimed at mathem

Achieve faster and more efficient network design and optimization with this comprehensive guide. Some of the most prominent researchers in the field explain the very latest analytic techniques and results from stochastic geometry for modelling the signal-to-interference-plus-noise ratio (SINR) distribution in heterogeneous cellular networks. This book will help readers to understand the effects of combining different system deployment parameters on key performance indicators such as coverage and capacity, enabling the efficient allocation of simulation resources. In addition to covering results for network models based on the Poisson point process, this book presents recent results for when non-Poisson base station configurations appear Poisson, due to random propagation effects such as fading and shadowing, as well as non-Poisson models for base station configurations, with a focus on determinantal point processes and tractable approximation methods. Theoretical results are illustrate

This book, dedicated to Winfried Stute on the occasion of his 70th birthday, presents a unique collection of contributions by leading experts in statistics, stochastic processes, mathematical finance

The Poisson process, a core object in modern probability, enjoys a richer theory than is sometimes appreciated. This volume develops the theory in the setting of a general abstract measure space, establishing basic results and properties as well as certain advanced topics in the stochastic analysis of the Poisson process. Also discussed are applications and related topics in stochastic geometry, including stationary point processes, the Boolean model, the Gilbert graph, stable allocations, and hyperplane processes. Comprehensive, rigorous, and self-contained, this text is ideal for graduate courses or for self-study, with a substantial number of exercises for each chapter. Mathematical prerequisites, mainly a sound knowledge of measure-theoretic probability, are kept in the background, but are reviewed comprehensively in the appendix. The authors are well-known researchers in probability theory; especially stochastic geometry. Their approach is informed both by their research and by th

The Poisson process, a core object in modern probability, enjoys a richer theory than is sometimes appreciated. This volume develops the theory in the setting of a general abstract measure space, establishing basic results and properties as well as certain advanced topics in the stochastic analysis of the Poisson process. Also discussed are applications and related topics in stochastic geometry, including stationary point processes, the Boolean model, the Gilbert graph, stable allocations, and hyperplane processes. Comprehensive, rigorous, and self-contained, this text is ideal for graduate courses or for self-study, with a substantial number of exercises for each chapter. Mathematical prerequisites, mainly a sound knowledge of measure-theoretic probability, are kept in the background, but are reviewed comprehensively in the appendix. The authors are well-known researchers in probability theory; especially stochastic geometry. Their approach is informed both by their research and by th

This text is devoted to the development of certain probabilistic methods in the specific field of stochastic differential equations and limit theorems for Markov processes. Specialists, researchers, a

This book introduces and applies the stochastic modeling techniques and the first exit time theory in demography through describing the theory related to the health state of a population and the intro

Continuous-Time Models in Corporate Finance synthesizes four decades of research to show how stochastic calculus can be used in corporate finance. Combining mathematical rigor with economic intuition,

This book provides a comprehensive and unified introduction to stochastic differential equations and related optimal control problems. The material is new and the presentation is reader-friendly. A ma

"This book focuses on the application of the methods organized in statistical physics, fuzzy logic, neuro nets and combinatorial stochastic processes which have been proven useful in analyzing complex

This book deals with the various aspects of stochastic dynamics, the resolution of large mechanical systems, and inverse problems. It integrates the most recent ideas from research and industry in the

This contributed volume comprises research articles and reviews on topics connected to the mathematical modeling of cellular systems. These contributions cover signaling pathways, stochastic effects,

This book presents the fundamental notions and advanced mathematical tools in the stochastic modeling of uncertainties and their quantification for large-scale computational models in sciences and eng

The book features new directions in analysis, with an emphasis on Hilbert space, mathematical physics, and stochastic processes. We interpret "non-commutative analysis" broadly to include re

The book features new directions in analysis, with an emphasis on Hilbert space, mathematical physics, and stochastic processes. We interpret "non-commutative analysis" broadly to include re

One of the major problems of macroeconomic theory is the way in which the people exchange goods in decentralized market economies. There are major disagreements among macroeconomists regarding tools to influence required outcomes. Since the mainstream efficient market theory fails to provide an internal coherent framework, there is a need for an alternative theory. The book provides an innovative approach for the analysis of agent based models, populated by the heterogeneous and interacting agents in the field of financial fragility. The text is divided in two parts; the first presents analytical developments of stochastic aggregation and macro-dynamics inference methods. The second part introduces macroeconomic models of financial fragility for complex systems populated by heterogeneous and interacting agents. The concepts of financial fragility and macroeconomic dynamics are explained in detail in separate chapters. The statistical physics approach is applied to explain theories of m

Studying the fine properties of solutions to Stochastic (Partial) Differential Equations with reflection at a boundary, this book begins with a discussion of classical one-dimensional diffusions as th

This text develops the necessary background in probability theory underlying diverse treatments of stochastic processes and their wide-ranging applications. In this second edition, the text has been r

Mathematical finance is a vast subject and is an ever growing field that no single book can cover everything, nor should it try to do so. Following on from the detailed treatment on stochastic calculu

The aim of this work is to provide an introduction to the theory of non-autonomous and stochastic dynamical systems, with a focus on the importance of the theory in the Applied Sciences. The book wil

This volume contains the lecture notes of the two courses given by Davar Khoshnevisan and René Schilling, respectively, at the second edition of the Barcelona Summer School on Stochastic Analysis, hel

This book presents a novel approach to time series econometrics, which studies the behavior of nonlinear stochastic processes. This approach allows for an arbitrary dependence structure in the increme

This focuses on the developing field of building probability models with the power of symbolic algebra systems. The book combines the uses of symbolic algebra with probabilistic/stochastic application

Spatiotemporal Random Fields: Theory and Applications, Second Edition, provides readers with a new and updated edition of the text that explores the application of random field models and stochastic d

This book has developed over the past fifteen years from a modern course on stochastic chemical kinetics for graduate students in physics, chemistry and biology. The first part presents a systematic c

Multi-state models describe stochastic processes that consist of transitions between states over time, such as the three-state illness-death model. Interval-censored data is extremely common as the ex

This book deals with methods to evaluate scientific productivity. In the book statistical methods, deterministic and stochastic models and numerous indexes are discussed that will help the reader to u

This book is devoted to the history of Change of Time Methods (CTM), the connections of CTM to stochastic volatilities and finance, fundamental aspects of the theory of CTM, basic concepts, and its pr

Nucleation is a stochastic process that occurs as the first step in the formation of a new thermodynamic phase. Understanding nucleation is important for numerous practical applications such as prepar

This book introduces and studies a number of stochastic models of subsistence, communication, social evolution and political transition that will allow the reader to grasp the role of uncertainty as a

The authors develop and estimate a stochastic dynamic programming model to analyze the relationship between compensation, including retirement benefits, and retention over the career of Chicago public

“Degradation process” refers to many types of reliability models, which correspond to various kinds of stochastic processes used for deterioration modeling. ?This book focuses on the case of a univari

Flow of ions through voltage gatedchannels can be represented theoretically using stochastic differentialequations where the gating mechanism is represented by a Markov model. The flow through achanne

The aim of this work is to present a unified approach to the modern field of control theory and to provide a technique for making problems involving deterministic, stochastic, and adaptive processes o

This book is devoted to the study of discrete q-distributions defined on the stochastic model of a sequence of independent Bernoulli trials. The mathematical prerequisites are modest, and the au

This monograph is a progressive introduction to non-commutativity in probability theory, summarizing and synthesizing recent results about classical and quantum stochastic processes on Lie algebras. In the early chapters, focus is placed on concrete examples of the links between algebraic relations and the moments of probability distributions. The subsequent chapters are more advanced and deal with Wigner densities for non-commutative couples of random variables, non-commutative stochastic processes with independent increments (quantum Lévy processes), and the quantum Malliavin calculus. This book will appeal to advanced undergraduate and graduate students interested in the relations between algebra, probability, and quantum theory. It also addresses a more advanced audience by covering other topics related to non-commutativity in stochastic calculus, Lévy processes, and the Malliavin calculus.

Dynamic stochastic general equilibrium (DSGE) models have become one of the workhorses of modern macroeconomics and are extensively used for academic research as well as forecasting and policy analysi

Mark H.A. Davis introduced the Piecewise-Deterministic Markov Process (PDMP) class of stochastic hybrid models in an article in 1984. Today it is used to model a variety of complex systems in the fiel

This book records a unique attempt over a ten-year period to use stochastic optimization in the natural language processing domain. Setting the work against the background of the logical rule-based ap