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46 results in Applied probability and stochastic networks

Page 1 of 3

Dynamics on Graphs
  • 2nd edition
  • Rick Durrett
  • Coming soon
  • Expected online publication date:
    September 2025
  • This extensive revision of the 2007 book 'Random Graph Dynamics,' covering the current state of mathematical research in the field, is ideal for researchers and graduate students. It considers a small number of types of graphs, primarily the configuration model and inhomogeneous random graphs. However, it investigates a wide variety of dynamics. The author describes results for the convergence to equilibrium for random walks on random graphs as well as topics that have emerged as mature research areas since the publication of the first edition, such as epidemics, the contact process, voter models, and coalescing random walk. Chapter 8 discusses a new challenging and largely uncharted direction: systems in which the graph and the states of their vertices coevolve.

Play of Chance and Purpose
  • An Invitation to Probability, Statistics, and Stochasticity Using Simulations and Projects
  • Amrik Sen
  • Coming soon
  • Expected online publication date:
    August 2025
    Print publication:
    30 September 2025
  • Play of Chance and Purpose emphasizes learning probability, statistics, and stochasticity by developing intuition and fostering imagination as a pedagogical approach. This book is meant for undergraduate and graduate students of basic sciences, applied sciences, engineering, and social sciences as an introduction to fundamental as well as advanced topics. The text has evolved out of the author's experience of teaching courses on probability, statistics, and stochastic processes at both undergraduate and graduate levels in India and the United States. Readers will get an opportunity to work on several examples from real-life applications and pursue projects and case-study analyses as capstone exercises in each chapter. Many projects involve the development of visual simulations of complex stochastic processes. This will augment the learners' comprehension of the subject and consequently train them to apply their learnings to solve hitherto unseen problems in science and engineering.

Partially Observed Markov Decision Processes
  • Filtering, Learning and Controlled Sensing
  • 2nd edition
  • Vikram Krishnamurthy
  • Published online:
    16 May 2025
    Print publication:
    05 June 2025
  • Covering formulation, algorithms and structural results and linking theory to real-world applications in controlled sensing (including social learning, adaptive radars and sequential detection), this book focuses on the conceptual foundations of partially observed Markov decision processes (POMDPs). It emphasizes structural results in stochastic dynamic programming, enabling graduate students and researchers in engineering, operations research, and economics to understand the underlying unifying themes without getting weighed down by mathematical technicalities. In light of major advances in machine learning over the past decade, this edition includes a new Part V on inverse reinforcement learning as well as a new chapter on non-parametric Bayesian inference (for Dirichlet processes and Gaussian processes), variational Bayes and conformal prediction.

Scalable Monte Carlo for Bayesian Learning
  • Paul Fearnhead, Christopher Nemeth, Chris J. Oates, Chris Sherlock
  • Published online:
    16 May 2025
    Print publication:
    05 June 2025
  • A graduate-level introduction to advanced topics in Markov chain Monte Carlo (MCMC), as applied broadly in the Bayesian computational context. The topics covered have emerged as recently as the last decade and include stochastic gradient MCMC, non-reversible MCMC, continuous time MCMC, and new techniques for convergence assessment. A particular focus is on cutting-edge methods that are scalable with respect to either the amount of data, or the data dimension, motivated by the emerging high-priority application areas in machine learning and AI. Examples are woven throughout the text to demonstrate how scalable Bayesian learning methods can be implemented. This text could form the basis for a course and is sure to be an invaluable resource for researchers in the field.

Random Graphs and Complex Networks
  • Volume 2
  • Remco van der Hofstad
  • Published online:
    08 February 2024
    Print publication:
    08 February 2024
  • Complex networks are key to describing the connected nature of the society that we live in. This book, the second of two volumes, describes the local structure of random graph models for real-world networks and determines when these models have a giant component and when they are small-, and ultra-small, worlds. This is the first book to cover the theory and implications of local convergence, a crucial technique in the analysis of sparse random graphs. Suitable as a resource for researchers and PhD-level courses, it uses examples of real-world networks, such as the Internet and citation networks, as motivation for the models that are discussed, and includes exercises at the end of each chapter to develop intuition. The book closes with an extensive discussion of related models and problems that demonstratemodern approaches to network theory, such as community structure and directed models.

Introduction to Probability for Computing
  • Mor Harchol-Balter
  • Published online:
    12 September 2023
    Print publication:
    28 September 2023
  • Learn about probability as it is used in computer science with this rigorous, yet highly accessible, undergraduate textbook. Fundamental probability concepts are explained in depth, prerequisite mathematics is summarized, and a wide range of computer science applications is described. Throughout, the material is presented in a “question and answer” style designed to encourage student engagement and understanding. Replete with almost 400 exercises, real-world computer science examples, and covering a wide range of topics from simulation with computer science workloads, to statistical inference, to randomized algorithms, to Markov models and queues, this interactive text is an invaluable learning tool whether your course covers probability with statistics, with stochastic processes, with randomized algorithms, or with simulation. The teaching package includes solutions, lecture slides, and lecture notes for students.

Bayesian Filtering and Smoothing
  • 2nd edition
  • Simo Särkkä, Lennart Svensson
  • Published online:
    01 June 2023
    Print publication:
    15 June 2023
  • Now in its second edition, this accessible text presents a unified Bayesian treatment of state-of-the-art filtering, smoothing, and parameter estimation algorithms for non-linear state space models. The book focuses on discrete-time state space models and carefully introduces fundamental aspects related to optimal filtering and smoothing. In particular, it covers a range of efficient non-linear Gaussian filtering and smoothing algorithms, as well as Monte Carlo-based algorithms. This updated edition features new chapters on constructing state space models of practical systems, the discretization of continuous-time state space models, Gaussian filtering by enabling approximations, posterior linearization filtering, and the corresponding smoothers. Coverage of key topics is expanded, including extended Kalman filtering and smoothing, and parameter estimation. The book's practical, algorithmic approach assumes only modest mathematical prerequisites, suitable for graduate and advanced undergraduate students. Many examples are included, with Matlab and Python code available online, enabling readers to implement algorithms in their own projects.

Network Models for Data Science
  • Theory, Algorithms, and Applications
  • Alan Julian Izenman
  • Published online:
    22 March 2023
    Print publication:
    05 January 2023
  • This text on the theory and applications of network science is aimed at beginning graduate students in statistics, data science, computer science, machine learning, and mathematics, as well as advanced students in business, computational biology, physics, social science, and engineering working with large, complex relational data sets. It provides an exciting array of analysis tools, including probability models, graph theory, and computational algorithms, exposing students to ways of thinking about types of data that are different from typical statistical data. Concepts are demonstrated in the context of real applications, such as relationships between financial institutions, between genes or proteins, between neurons in the brain, and between terrorist groups. Methods and models described in detail include random graph models, percolation processes, methods for sampling from huge networks, network partitioning, and community detection. In addition to static networks the book introduces dynamic networks such as epidemics, where time is an important component.

The Fundamentals of Heavy Tails
  • Properties, Emergence, and Estimation
  • Jayakrishnan Nair, Adam Wierman, Bert Zwart
  • Published online:
    17 May 2022
    Print publication:
    09 June 2022
  • Heavy tails –extreme events or values more common than expected –emerge everywhere: the economy, natural events, and social and information networks are just a few examples. Yet after decades of progress, they are still treated as mysterious, surprising, and even controversial, primarily because the necessary mathematical models and statistical methods are not widely known. This book, for the first time, provides a rigorous introduction to heavy-tailed distributions accessible to anyone who knows elementary probability. It tackles and tames the zoo of terminology for models and properties, demystifying topics such as the generalized central limit theorem and regular variation. It tracks the natural emergence of heavy-tailed distributions from a wide variety of general processes, building intuition. And it reveals the controversy surrounding heavy tails to be the result of flawed statistics, then equips readers to identify and estimate with confidence. Over 100 exercises complete this engaging package.

Large-Scale System Analysis Under Uncertainty
  • With Electric Power Applications
  • Alejandro D. Domínguez-García
  • Published online:
    17 January 2022
    Print publication:
    17 February 2022
  • Discover a comprehensive set of tools and techniques for analyzing the impact of uncertainty on large-scale engineered systems. Providing accessible yet rigorous coverage, it showcases the theory through detailed case studies drawn from electric power application problems, including the impact of integration of renewable-based power generation in bulk power systems, the impact of corrupted measurement and communication devices in microgrid closed-loop controls, and the impact of components failures on the reliability of power supply systems. The case studies also serve as a guide on how to tackle similar problems that appear in other engineering application domains, including automotive and aerospace engineering. This is essential reading for academic researchers and graduate students in power systems engineering, and dynamic systems and control engineering.

Scheduling and Control of Queueing Networks
  • Gideon Weiss
  • Published online:
    01 October 2021
    Print publication:
    14 October 2021
  • Applications of queueing network models have multiplied in the last generation, including scheduling of large manufacturing systems, control of patient flow in health systems, load balancing in cloud computing, and matching in ride sharing. These problems are too large and complex for exact solution, but their scale allows approximation. This book is the first comprehensive treatment of fluid scaling, diffusion scaling, and many-server scaling in a single text presented at a level suitable for graduate students. Fluid scaling is used to verify stability, in particular treating max weight policies, and to study optimal control of transient queueing networks. Diffusion scaling is used to control systems in balanced heavy traffic, by solving for optimal scheduling, admission control, and routing in Brownian networks. Many-server scaling is studied in the quality and efficiency driven Halfin–Whitt regime and applied to load balancing in the supermarket model and to bipartite matching in ride-sharing applications.

Thinking Probabilistically
  • Stochastic Processes, Disordered Systems, and Their Applications
  • Ariel Amir
  • Published online:
    15 December 2020
    Print publication:
    17 December 2020
  • Probability theory has diverse applications in a plethora of fields, including physics, engineering, computer science, chemistry, biology and economics. This book will familiarize students with various applications of probability theory, stochastic modeling and random processes, using examples from all these disciplines and more. The reader learns via case studies and begins to recognize the sort of problems that are best tackled probabilistically. The emphasis is on conceptual understanding, the development of intuition and gaining insight, keeping technicalities to a minimum. Nevertheless, a glimpse into the depth of the topics is provided, preparing students for more specialized texts while assuming only an undergraduate-level background in mathematics. The wide range of areas covered - never before discussed together in a unified fashion – includes Markov processes and random walks, Langevin and Fokker–Planck equations, noise, generalized central limit theorem and extreme values statistics, random matrix theory and percolation theory.

Processing Networks
  • Fluid Models and Stability
  • J. G. Dai, J. Michael Harrison
  • Published online:
    17 September 2020
    Print publication:
    15 October 2020
  • This state-of-the-art account unifies material developed in journal articles over the last 35 years, with two central thrusts: It describes a broad class of system models that the authors call 'stochastic processing networks' (SPNs), which include queueing networks and bandwidth sharing networks as prominent special cases; and in that context it explains and illustrates a method for stability analysis based on fluid models. The central mathematical result is a theorem that can be paraphrased as follows: If the fluid model derived from an SPN is stable, then the SPN itself is stable. Two topics discussed in detail are (a) the derivation of fluid models by means of fluid limit analysis, and (b) stability analysis for fluid models using Lyapunov functions. With regard to applications, there are chapters devoted to max-weight and back-pressure control, proportionally fair resource allocation, data center operations, and flow management in packet networks. Geared toward researchers and graduate students in engineering and applied mathematics, especially in electrical engineering and computer science, this compact text gives readers full command of the methods.

The Probability Companion for Engineering and Computer Science
  • Adam Prügel-Bennett
  • Published online:
    03 January 2020
    Print publication:
    23 January 2020
  • This friendly guide is the companion you need to convert pure mathematics into understanding and facility with a host of probabilistic tools. The book provides a high-level view of probability and its most powerful applications. It begins with the basic rules of probability and quickly progresses to some of the most sophisticated modern techniques in use, including Kalman filters, Monte Carlo techniques, machine learning methods, Bayesian inference and stochastic processes. It draws on thirty years of experience in applying probabilistic methods to problems in computational science and engineering, and numerous practical examples illustrate where these techniques are used in the real world. Topics of discussion range from carbon dating to Wasserstein GANs, one of the most recent developments in Deep Learning. The underlying mathematics is presented in full, but clarity takes priority over complete rigour, making this text a starting reference source for researchers and a readable overview for students.

Stochastic Modelling of Reaction–Diffusion Processes
  • Radek Erban, S. Jonathan Chapman
  • Published online:
    04 November 2019
    Print publication:
    30 January 2020
  • This practical introduction to stochastic reaction-diffusion modelling is based on courses taught at the University of Oxford. The authors discuss the essence of mathematical methods which appear (under different names) in a number of interdisciplinary scientific fields bridging mathematics and computations with biology and chemistry. The book can be used both for self-study and as a supporting text for advanced undergraduate or beginning graduate-level courses in applied mathematics. New mathematical approaches are explained using simple examples of biological models, which range in size from simulations of small biomolecules to groups of animals. The book starts with stochastic modelling of chemical reactions, introducing stochastic simulation algorithms and mathematical methods for analysis of stochastic models. Different stochastic spatio-temporal models are then studied, including models of diffusion and stochastic reaction-diffusion modelling. The methods covered include molecular dynamics, Brownian dynamics, velocity jump processes and compartment-based (lattice-based) models.

Applied Stochastic Differential Equations
  • Simo Särkkä, Arno Solin
  • Published online:
    16 April 2019
    Print publication:
    02 May 2019
  • Stochastic differential equations are differential equations whose solutions are stochastic processes. They exhibit appealing mathematical properties that are useful in modeling uncertainties and noisy phenomena in many disciplines. This book is motivated by applications of stochastic differential equations in target tracking and medical technology and, in particular, their use in methodologies such as filtering, smoothing, parameter estimation, and machine learning. It builds an intuitive hands-on understanding of what stochastic differential equations are all about, but also covers the essentials of Itô calculus, the central theorems in the field, and such approximation schemes as stochastic Runge–Kutta. Greater emphasis is given to solution methods than to analysis of theoretical properties of the equations. The book's practical approach assumes only prior understanding of ordinary differential equations. The numerous worked examples and end-of-chapter exercises include application-driven derivations and computational assignments. MATLAB/Octave source code is available for download, promoting hands-on work with the methods.

Stochastic Geometry Analysis of Cellular Networks
  • Bartłomiej Błaszczyszyn, Martin Haenggi, Paul Keeler, Sayandev Mukherjee
  • Published online:
    26 March 2018
    Print publication:
    19 April 2018
  • 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 illustrated with practical Long-Term Evolution (LTE) applications and compared with real-world deployment results.

Introduction to Hidden Semi-Markov Models
  • John van der Hoek, Robert J. Elliott
  • Published online:
    01 February 2018
    Print publication:
    08 February 2018
  • Markov chains and hidden Markov chains have applications in many areas of engineering and genomics. This book provides a basic introduction to the subject by first developing the theory of Markov processes in an elementary discrete time, finite state framework suitable for senior undergraduates and graduates. The authors then introduce semi-Markov chains and hidden semi-Markov chains, before developing related estimation and filtering results. Genomics applications are modelled by discrete observations of these hidden semi-Markov chains. This book contains new results and previously unpublished material not available elsewhere. The approach is rigorous and focused on applications.

Computational Phylogenetics
  • An Introduction to Designing Methods for Phylogeny Estimation
  • Tandy Warnow
  • Published online:
    26 October 2017
    Print publication:
    02 November 2017
  • A comprehensive account of both basic and advanced material in phylogeny estimation, focusing on computational and statistical issues. No background in biology or computer science is assumed, and there is minimal use of mathematical formulas, meaning that students from many disciplines, including biology, computer science, statistics, and applied mathematics, will find the text accessible. The mathematical and statistical foundations of phylogeny estimation are presented rigorously, following which more advanced material is covered. This includes substantial chapters on multi-locus phylogeny estimation, supertree methods, multiple sequence alignment techniques, and designing methods for large-scale phylogeny estimation. The author provides key analytical techniques to prove theoretical properties about methods, as well as addressing performance in practice for methods for estimating trees. Research problems requiring novel computational methods are also presented, so that graduate students and researchers from varying disciplines will be able to enter the broad and exciting field of computational phylogenetics.

Random Graphs and Complex Networks
  • Remco van der Hofstad
  • Published online:
    12 January 2017
    Print publication:
    22 December 2016
  • This rigorous introduction to network science presents random graphs as models for real-world networks. Such networks have distinctive empirical properties and a wealth of new models have emerged to capture them. Classroom tested for over ten years, this text places recent advances in a unified framework to enable systematic study. Designed for a master's-level course, where students may only have a basic background in probability, the text covers such important preliminaries as convergence of random variables, probabilistic bounds, coupling, martingales, and branching processes. Building on this base - and motivated by many examples of real-world networks, including the Internet, collaboration networks, and the World Wide Web - it focuses on several important models for complex networks and investigates key properties, such as the connectivity of nodes. Numerous exercises allow students to develop intuition and experience in working with the models.

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