Search results for: first-look-at-stochastic-processes-a

A First Look At Stochastic Processes

Author : Rosenthal Jeffrey S
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This textbook introduces the theory of stochastic processes, that is, randomness which proceeds in time. Using concrete examples like repeated gambling and jumping frogs, it presents fundamental mathematical results through simple, clear, logical theorems and examples. It covers in detail such essential material as Markov chain recurrence criteria, the Markov chain convergence theorem, and optional stopping theorems for martingales. The final chapter provides a brief introduction to Brownian motion, Markov processes in continuous time and space, Poisson processes, and renewal theory.Interspersed throughout are applications to such topics as gambler's ruin probabilities, random walks on graphs, sequence waiting times, branching processes, stock option pricing, and Markov Chain Monte Carlo (MCMC) algorithms.The focus is always on making the theory as well-motivated and accessible as possible, to allow students and readers to learn this fascinating subject as easily and painlessly as possible.

A First Look at Rigorous Probability Theory

Author : Jeffrey S Rosenthal
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Solutions Manual for Free Download This textbook is an introduction to probability theory using measure theory. It is designed for graduate students in a variety of fields (mathematics, statistics, economics, management, finance, computer science, and engineering) who require a working knowledge of probability theory that is mathematically precise, but without excessive technicalities. The text provides complete proofs of all the essential introductory results. Nevertheless, the treatment is focused and accessible, with the measure theory and mathematical details presented in terms of intuitive probabilistic concepts, rather than as separate, imposing subjects. In this new edition, many exercises and small additional topics have been added and existing ones expanded. The text strikes an appropriate balance, rigorously developing probability theory while avoiding unnecessary detail.

A First Look at Rigorous Probability Theory

Author : Jeffrey S. Rosenthal
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This textbook is an introduction to rigorous probability theory using measure theory. It provides rigorous, complete proofs of all the essential introductory mathematical results of probability theory and measure theory. More advanced or specialized areas are entirely omitted or only hinted at. For example, the text includes a complete proof of the classical central limit theorem, including the necessary continuity theorem for characteristic functions, but the more general Lindeberg central limit theorem is only outlined and is not proved. Similarly, all necessary facts from measure theory are proved before they are used, but more abstract or advanced measure theory results are not included. Furthermore, measure theory is discussed as much as possible purely in terms of probability, as opposed to being treated as a separate subject which must be mastered before probability theory can be understood.

Homeostatic Mechanisms

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A First Course in Stochastic Processes

Author : Samuel Karlin
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A First Course in Stochastic Processes focuses on several principal areas of stochastic processes and the diversity of applications of stochastic processes, including Markov chains, Brownian motion, and Poisson processes. The publication first takes a look at the elements of stochastic processes, Markov chains, and the basic limit theorem of Markov chains and applications. Discussions focus on criteria for recurrence, absorption probabilities, discrete renewal equation, classification of states of a Markov chain, and review of basic terminologies and properties of random variables and distribution functions. The text then examines algebraic methods in Markov chains and ratio theorems of transition probabilities and applications. The manuscript elaborates on the sums of independent random variables as a Markov chain, classical examples of continuous time Markov chains, and continuous time Markov chains. Topics include differentiability properties of transition probabilities, birth and death processes with absorbing states, general pure birth processes and Poisson processes, and recurrence properties of sums of independent random variables. The book then ponders on Brownian motion, compounding stochastic processes, and deterministic and stochastic genetic and ecological processes. The publication is a valuable source of information for readers interested in stochastic processes.

Probability Statistics and Stochastic Processes

Author : Peter Olofsson
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Praise for the First Edition ". . . an excellent textbook . . . well organized and neatly written." —Mathematical Reviews ". . . amazingly interesting . . ." —Technometrics Thoroughly updated to showcase the interrelationships between probability, statistics, and stochastic processes, Probability, Statistics, and Stochastic Processes, Second Edition prepares readers to collect, analyze, and characterize data in their chosen fields. Beginning with three chapters that develop probability theory and introduce the axioms of probability, random variables, and joint distributions, the book goes on to present limit theorems and simulation. The authors combine a rigorous, calculus-based development of theory with an intuitive approach that appeals to readers' sense of reason and logic. Including more than 400 examples that help illustrate concepts and theory, the Second Edition features new material on statistical inference and a wealth of newly added topics, including: Consistency of point estimators Large sample theory Bootstrap simulation Multiple hypothesis testing Fisher's exact test and Kolmogorov-Smirnov test Martingales, renewal processes, and Brownian motion One-way analysis of variance and the general linear model Extensively class-tested to ensure an accessible presentation, Probability, Statistics, and Stochastic Processes, Second Edition is an excellent book for courses on probability and statistics at the upper-undergraduate level. The book is also an ideal resource for scientists and engineers in the fields of statistics, mathematics, industrial management, and engineering.

Stochastic Processes and Applications

Author : Jacek Fabian
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The field of stochastic processes is essentially a branch of probability theory, treating probabilistic models that evolve in time. It is best viewed as a branch of mathematics, starting with the axioms of probability and containing a rich and fascinating set of results following from those axioms. Although the results are applicable to many areas, they are best understood initially in terms of their mathematical structure and interrelationships. Applying axiomatic probability results to a real-world area requires creating a probability model for the given area. Stochastic processes were first studied rigorously in the late 19th century to aid in understanding financial markets and Brownian motion. These subjects originally had an application emphasis, the first on queueing and congestion in data networks and the second on modulation and detection of signals in the presence of noise. It has become increasingly clear that the mathematical development is applicable to a much broader set of applications in engineering, operations research, physics, biology, economics, finance, statistics, etc. Stochastic Processes and their Applications emphasizes on the theory and applications of stochastic processes. It is concerned with concepts and techniques, and is oriented towards a broad spectrum of mathematical, scientific and engineering interests. Characterization, structural properties, inference and control of stochastic processes are covered.

NASA Reference Publication

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An Introduction to Stochastic Processes

Author : Edward P. C. Kao
File Size : 76.43 MB
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Intended for a calculus-based course in stochastic processes at the graduate or advanced undergraduate level, this text offers a modern, applied perspective. Instead of the standard formal and mathematically rigorous approach usual for texts for this course, Edward Kao emphasizes the development of operational skills and analysis through a variety of well-chosen examples.

The Spectral Analysis of Time Series

Author : Lambert Herman Koopmans
File Size : 39.24 MB
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The Spectral Analysis of Time Series ...

The Generic Chaining

Author : Michel Talagrand
File Size : 80.10 MB
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The fundamental question of characterizing continuity and boundedness of Gaussian processes goes back to Kolmogorov. After contributions by R. Dudley and X. Fernique, it was solved by the author. This book provides an overview of "generic chaining", a completely natural variation on the ideas of Kolmogorov. It takes the reader from the first principles to the edge of current knowledge and to the open problems that remain in this domain.

Semiconductor Physics

Author : Sandip Tiwari
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This text brings together traditional solid-state approaches from the 20th century with developments of the early part of the 21st century, to reach an understanding of semiconductor physics in its multifaceted forms. It reveals how an understanding of what happens within the material can lead to insights into what happens in its use.

Stochastic Processes

Author : Sheldon M. Ross
File Size : 64.41 MB
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A nonmeasure theoretic introduction to stochastic processes. Considers its diverse range of applications and provides readers with probabilistic intuition and insight in thinking about problems. This revised edition contains additional material on compound Poisson random variables including an identity which can be used to efficiently compute moments; a new chapter on Poisson approximations; and coverage of the mean time spent in transient states as well as examples relating to the Gibb's sampler, the Metropolis algorithm and mean cover time in star graphs. Numerous exercises and problems have been added throughout the text.

Applied statistics

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Stochastic Processes and Their First Passage Times

Author : M. T. Wasan
File Size : 90.87 MB
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Proceedings of the Summer Research Institute on Statistical Inference for Stochastic Processes Bloomington Indiana July 31 August 9 1974 Stochastic processes and related topics

Author : Madan Lal Puri
File Size : 80.1 MB
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Stochastic Processes and Random Vibrations

Author : Júlíus Sólnes
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Beginning with the basics of probability and an overview of stochastic process, this book goes on to explore their engineering applications: random vibration and system analysis. It addresses extreme conditions such as distribution of large vibration peaks, probabilities of exceeding certain limits, and fatigue. Includes numerous tested examples: earthquake risk analysis, distribution of extreme wind speeds, analysis of structural reliability, earthquake response of tall multi-storey structure and wind loading of tall towers.

An Introduction to Stochastic Processes

Author : M. T. Wasan
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Agent Based and Individual Based Modeling

Author : Steven F. Railsback
File Size : 47.38 MB
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The essential textbook on agent-based modeling—now fully updated and expanded Agent-Based and Individual-Based Modeling has become the standard textbook on the subject for classroom use and self-instruction. Drawing on the latest version of NetLogo and fully updated with new examples, exercises, and an enhanced text for easier comprehension, this is the essential resource for anyone seeking to understand how the dynamics of biological, social, and other complex systems arise from the characteristics of the agents that make up these systems. Steven Railsback and Volker Grimm lead students stepwise through the processes of designing, programming, documenting, and doing scientific research with agent-based models, focusing on the adaptive behaviors that make these models necessary. They cover the fundamentals of modeling and model analysis, introduce key modeling concepts, and demonstrate how to implement them using NetLogo. They also address pattern-oriented modeling, an invaluable strategy for modeling real-world problems and developing theory. This accessible and authoritative book focuses on modeling as a tool for understanding real complex systems. It explains how to pose a specific question, use observations from actual systems to design models, write and test software, and more. A hands-on introduction that guides students from conceptual design to computer implementation to analysis Filled with new examples and exercises and compatible with the latest version of NetLogo Ideal for students and researchers across the natural and social sciences Written by two leading practitioners Supported by extensive instructional materials at www.railsback-grimm-abm-book.com

Brookhaven Symposia in Biology

Author : Brookhaven National Laboratory
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