Stochastic Methods

This book collects lectures and research results in stochastic analysis by distinguished researchers, invited on the occasion of a thematic semester organized by the Bernoulli Center of the Ecole Poly

This monograph is concerned with the analysis and numerical solution of a stochastic inverse anomaly detection problem in electrical impedance tomography (EIT). Martin Simon studies the problem of det

This volume features a collection of contributed articles and lecture notes from the XI Symposium on Probability and Stochastic Processes, held at CIMAT Mexico in September 2013. Since this year's sym

This book presents the novel formulation and development of a Stochastic Flood Forecasting System, using the Middle River Vistula basin in Poland as a case study. The system has a modular structure, i

This textbook on elementary stochastic calculus is designed for senior undergraduate students in math, economics, and business. Although the material is presented at an introductory level, students sh

This SpringerBrief presents research in the application of Stochastic Petri Nets (SPN) to the performance evaluation of wireless networks under bursty traffic. It covers typical Quality-of-Service per

The vast majority of random processes in the real world have no memory - the next step in their development depends purely on their current state. Stochastic realizations are therefore defined purely

This volume in the Mastering Mathematical Finance series strikes just the right balance between mathematical rigour and practical application. Existing books on the challenging subject of stochastic interest rate models are often too advanced for Master's students or fail to include practical examples. Stochastic Interest Rates covers practical topics such as calibration, numerical implementation and model limitations in detail. The authors provide numerous exercises and carefully chosen examples to help students acquire the necessary skills to deal with interest rate modelling in a real-world setting. In addition, the book's webpage at www.cambridge.org/9781107002579 provides solutions to all of the exercises as well as the computer code (and associated spreadsheets) for all numerical work, which allows students to verify the results.

Based on a starter course for beginning graduate students, Core Statistics provides concise coverage of the fundamentals of inference for parametric statistical models, including both theory and practical numerical computation. The book considers both frequentist maximum likelihood and Bayesian stochastic simulation while focusing on general methods applicable to a wide range of models and emphasizing the common questions addressed by the two approaches. This compact package serves as a lively introduction to the theory and tools that a beginning graduate student needs in order to make the transition to serious statistical analysis: inference; modeling; computation, including some numerics; and the R language. Aimed also at any quantitative scientist who uses statistical methods, this book will deepen readers' understanding of why and when methods work and explain how to develop suitable methods for non-standard situations, such as in ecology, big data and genomics.

Based on a starter course for beginning graduate students, Core Statistics provides concise coverage of the fundamentals of inference for parametric statistical models, including both theory and practical numerical computation. The book considers both frequentist maximum likelihood and Bayesian stochastic simulation while focusing on general methods applicable to a wide range of models and emphasizing the common questions addressed by the two approaches. This compact package serves as a lively introduction to the theory and tools that a beginning graduate student needs in order to make the transition to serious statistical analysis: inference; modeling; computation, including some numerics; and the R language. Aimed also at any quantitative scientist who uses statistical methods, this book will deepen readers' understanding of why and when methods work and explain how to develop suitable methods for non-standard situations, such as in ecology, big data and genomics.

The book presents applications of stochastic calculus to derivative security pricing and interest rate modelling. By focusing more on the financial intuition of the applications rather than the mathem

This book is the first to comprehensively explore elasticity imaging and examines recent, important developments in asymptotic imaging, modeling, and analysis of deterministic and stochastic elastic w

Paul M. Geffert analyses the interplay of noise and time delay in non-excitable nonlinear systems and the modulation of stochastic effects. In particular, the author studies coherence resonance, which

This volume presents the latest advances and trends in stochastic models and related statistical procedures. Selected peer-reviewed contributions focus on statistical inference, quality control, chang

Encompassing both introductory and more advanced research material, these notes deal with the author's contributions to stochastic processes and focus on Brownian motion processes and its derivative w

A Practitioner's Guide to Stochastic Frontier Analysis Using Stata provides practitioners in academia and industry with a step-by-step guide on how to conduct efficiency analysis using the stochastic frontier approach. The authors explain in detail how to estimate production, cost, and profit efficiency and introduce the basic theory of each model in an accessible way, using empirical examples that demonstrate the interpretation and application of models. This book also provides computer code, allowing users to apply the models in their own work, and incorporates the most recent stochastic frontier models developed in academic literature. Such recent developments include models of heteroscedasticity and exogenous determinants of inefficiency, scaling models, panel models with time-varying inefficiency, growth models, and panel models that separate firm effects and persistent and transient inefficiency. Immensely helpful to applied researchers, this book bridges the chasm between theory

This volume contains pedagogical, review and research level papers on fractional stochastic and quantum processes which have been the focus of intensive mathematical, experimental, and computational s

Articles from many of the main contributors to recent progress in stochastic analysis are included in this volume, which provides a snapshot of the current state of the area and its ongoing developmen

A Practitioner's Guide to Stochastic Frontier Analysis Using Stata provides practitioners in academia and industry with a step-by-step guide on how to conduct efficiency analysis using the stochastic frontier approach. The authors explain in detail how to estimate production, cost, and profit efficiency and introduce the basic theory of each model in an accessible way, using empirical examples that demonstrate the interpretation and application of models. This book also provides computer code, allowing users to apply the models in their own work, and incorporates the most recent stochastic frontier models developed in academic literature. Such recent developments include models of heteroscedasticity and exogenous determinants of inefficiency, scaling models, panel models with time-varying inefficiency, growth models, and panel models that separate firm effects and persistent and transient inefficiency. Immensely helpful to applied researchers, this book bridges the chasm between theory

Considering Poisson random measures as the driving sources for stochastic (partial) differential equations allows us to incorporate jumps and to model sudden, unexpected phenomena. By using such equat

This volume is an attempt to provide a graduate level introduction to various aspects of stochastic geometry, spatial statistics and random fields, with special emphasis placed on fundamental classes

This book presents the latest findings on stochastic dynamic programming models and on solving optimal control problems in networks. It includes the authors’ new findings on determining the optimal so

This book offers a systematic introduction to the optimal stochastic control theory via the dynamic programming principle, which is a powerful tool to analyze control problems.First we consider comple

The book describes a systematic stochastic modeling approach for assessing thermal-fatigue crack-growth in mixing tees, based on the power spectral density of temperature fluctuation at the inner pipe

This book introduces differential stochastic equations and Malliavin calculus. The revised and expanded third edition offers corrections and improvements and a new section covering the differentiabili

A guide to stochastic calculus as the basis behind mathematical finance An increasingly popular field of study at universities and an essential skill for investment bank employees, mathematical finan

This book reveals the underlying mechanisms of complexity and stochastic evolutions of traffic flows. Using Eulerian and Lagrangian measurements, the authors propose lognormal headway/spacing/velocity

This book presents a systematic treatment of Markov chains, diffusion processes and state space models, as well as alternative approaches to Markov chains through stochastic difference equations and s

This book develops the theory of continuous and discrete stochastic processes within the context of cell biology. A wide range of biological topics are covered including normal and anomalous diffusion

In some cases, certain coherent structures can exist in stochastic dynamic systems almost in every particular realization of random parameters describing these systems. Dynamic localization in one-dim

This book brings theories in nonlinear dynamics, stochastic processes, irreversible thermodynamics, physical chemistry and biochemistry together in an introductory but formal and comprehensive manner.

Striking a balance between theory and practice, this graduate-level text is perfect for students in the applied sciences. The author provides a clear introduction to the classical methods, how they work and why they sometimes fail. Crucially, he also demonstrates how these simple and classical techniques can be combined to address difficult problems. Many worked examples and sample programs are provided to help the reader make practical use of the subject material. Further mathematical background, if required, is summarized in an appendix. Topics covered include classical methods for linear systems, eigenvalues, interpolation and integration, ODEs and data fitting, and also more modern ideas like adaptivity and stochastic differential equations.

This rigorous, self-contained book describes mathematical and, in particular, stochastic and graph theoretic methods to assess the performance of complex networks and systems. It comprises three parts: the first is a review of probability theory; Part II covers the classical theory of stochastic processes (Poisson, Markov and queueing theory), which are considered to be the basic building blocks for performance evaluation studies; Part III focuses on the rapidly expanding new field of network science. This part deals with the recently obtained insight that many very different large complex networks – such as the Internet, World Wide Web, metabolic and human brain networks, utility infrastructures, social networks – evolve and behave according to general common scaling laws. This understanding is useful when assessing the end-to-end quality of Internet services and when designing robust and secure networks. Containing problems and solved solutions, the book is ideal for graduate student

Communication networks underpin our modern world, and provide fascinating and challenging examples of large-scale stochastic systems. Randomness arises in communication systems at many levels: for example, the initiation and termination times of calls in a telephone network, or the statistical structure of the arrival streams of packets at routers in the Internet. How can routing, flow control and connection acceptance algorithms be designed to work well in uncertain and random environments? This compact introduction illustrates how stochastic models can be used to shed light on important issues in the design and control of communication networks. It will appeal to readers with a mathematical background wishing to understand this important area of application, and to those with an engineering background who want to grasp the underlying mathematical theory. Each chapter ends with exercises and suggestions for further reading.

Communication networks underpin our modern world, and provide fascinating and challenging examples of large-scale stochastic systems. Randomness arises in communication systems at many levels: for example, the initiation and termination times of calls in a telephone network, or the statistical structure of the arrival streams of packets at routers in the Internet. How can routing, flow control and connection acceptance algorithms be designed to work well in uncertain and random environments? This compact introduction illustrates how stochastic models can be used to shed light on important issues in the design and control of communication networks. It will appeal to readers with a mathematical background wishing to understand this important area of application, and to those with an engineering background who want to grasp the underlying mathematical theory. Each chapter ends with exercises and suggestions for further reading.

This book describes the stochastic dynamics modeling of gene expression processes not only at the cell level but also at higher organization levels, such as in morphogenesis. The book is one of the fi

This definitive textbook provides a solid introduction to discrete and continuous stochastic processes, tackling a complex field in a way that instils a deep understanding of the relevant mathematical principles, and develops an intuitive grasp of the way these principles can be applied to modelling real-world systems. It includes a careful review of elementary probability and detailed coverage of Poisson, Gaussian and Markov processes with richly varied queuing applications. The theory and applications of inference, hypothesis testing, estimation, random walks, large deviations, martingales and investments are developed. Written by one of the world's leading information theorists, evolving over twenty years of graduate classroom teaching and enriched by over 300 exercises, this is an exceptional resource for anyone looking to develop their understanding of stochastic processes.

Hopfner presents this volume of derivations of asymptotic statistics, with sections that also integrate stochastic processes but can be skipped to focus on statistics alone. The first chapter introduc

Starting from the premise that abstract quantum stochastic processes can be understood as a quantum field theory in one space and time coordinate, this guide considers a number of representative examp

In this book we analyze the error caused by numerical schemes for the approximation of semilinear stochastic evolution equations (SEEq) in a Hilbert space-valued setting. The numerical schemes conside