Essentials of Stochastic Processes

Filename: essentials-of-stochastic-processes.pdf
ISBN: 9783319456140
Release Date: 2016-11-07
Number of pages: 275
Author: Richard Durrett
Publisher: Springer

Download and read online Essentials of Stochastic Processes in PDF and EPUB Building upon the previous editions, this textbook is a first course in stochastic processes taken by undergraduate and graduate students (MS and PhD students from math, statistics, economics, computer science, engineering, and finance departments) who have had a course in probability theory. It covers Markov chains in discrete and continuous time, Poisson processes, renewal processes, martingales, and option pricing. One can only learn a subject by seeing it in action, so there are a large number of examples and more than 300 carefully chosen exercises to deepen the reader’s understanding. Drawing from teaching experience and student feedback, there are many new examples and problems with solutions that use TI-83 to eliminate the tedious details of solving linear equations by hand, and the collection of exercises is much improved, with many more biological examples. Originally included in previous editions, material too advanced for this first course in stochastic processes has been eliminated while treatment of other topics useful for applications has been expanded. In addition, the ordering of topics has been improved; for example, the difficult subject of martingales is delayed until its usefulness can be applied in the treatment of mathematical finance.


Essentials of Stochastic Processes

Filename: essentials-of-stochastic-processes.pdf
ISBN: 9781461436157
Release Date: 2012-05-19
Number of pages: 266
Author: Richard Durrett
Publisher: Springer Science & Business Media

Download and read online Essentials of Stochastic Processes in PDF and EPUB This book is for a first course in stochastic processes taken by undergraduates or master’s students who have had a course in probability theory. It covers Markov chains in discrete and continuous time, Poisson processes, renewal processes, martingales, and mathematical finance. One can only learn a subject by seeing it in action, so there are a large number of examples and more than 300 carefully chosen exercises to deepen the reader’s understanding The book has undergone a thorough revision since the first edition. There are many new examples and problems with solutions that use the TI-83 to eliminate the tedious details of solving linear equations by hand. Some material that was too advanced for the level has been eliminated while the treatment of other topics useful for applications has been expanded. In addition, the ordering of topics has been improved. For example, the difficult subject of martingales is delayed until its usefulness can be seen in the treatment of mathematical finance. Richard Durrett received his Ph.D. in Operations Research from Stanford in 1976. He taught at the UCLA math department for nine years and at Cornell for twenty-five before moving to Duke in 2010. He is the author of 8 books and almost 200 journal articles, and has supervised more that 40 Ph.D. students. Most of his current research concerns the applications of probability to biology: ecology, genetics, and most recently cancer.


Essentials of Stochastic Processes

Filename: essentials-of-stochastic-processes.pdf
ISBN: 331945613X
Release Date: 2016-12-01
Number of pages: 275
Author: Richard Durrett
Publisher: Springer

Download and read online Essentials of Stochastic Processes in PDF and EPUB Building upon the previous editions, this textbook is a first course in stochastic processes taken by undergraduate and graduate students (MS and PhD students from math, statistics, economics, computer science, engineering, and finance departments) who have had a course in probability theory. It covers Markov chains in discrete and continuous time, Poisson processes, renewal processes, martingales, and option pricing. One can only learn a subject by seeing it in action, so there are a large number of examples and more than 300 carefully chosen exercises to deepen the reader’s understanding. Drawing from teaching experience and student feedback, there are many new examples and problems with solutions that use TI-83 to eliminate the tedious details of solving linear equations by hand, and the collection of exercises is much improved, with many more biological examples. Originally included in previous editions, material too advanced for this first course in stochastic processes has been eliminated while treatment of other topics useful for applications has been expanded. In addition, the ordering of topics has been improved; for example, the difficult subject of martingales is delayed until its usefulness can be applied in the treatment of mathematical finance.


Essentials of Stochastic Processes

Filename: essentials-of-stochastic-processes.pdf
ISBN: 0821838989
Release Date: 2006
Number of pages: 171
Author: Kiyosi Itō
Publisher: American Mathematical Soc.

Download and read online Essentials of Stochastic Processes in PDF and EPUB This book is an English translation of Kiyosi Ito's monograph published in Japanese in 1957. It gives a unified and comprehensive account of additive processes (or Levy processes), stationary processes, and Markov processes, which constitute the three most important classes of stochastic processes. Written by one of the leading experts in the field, this volume presents to the reader lucid explanations of the fundamental concepts and basic results in each of these three major areas of the theory of stochastic processes. With the requirements limited to an introductory graduate course on analysis (especially measure theory) and basic probability theory, this book is an excellent text for any graduate course on stochastic processes. Kiyosi Ito is famous throughout the world for his work on stochastic integrals (including the Ito formula), but he has made substantial contributions to other areas of probability theory as well, such as additive processes, stationary processes, and Markov processes (especially diffusion processes), which are topics covered in this book. For his contributions and achievements, he has received, among others, the Wolf Prize, the Japan Academy Prize, and the Kyoto Prize.


Essentials of Stochastic Finance

Filename: essentials-of-stochastic-finance.pdf
ISBN: 9789814495660
Release Date: 1999-01-15
Number of pages: 852
Author: Albert N Shiryaev
Publisher: World Scientific

Download and read online Essentials of Stochastic Finance in PDF and EPUB This important book provides information necessary for those dealing with stochastic calculus and pricing in the models of financial markets operating under uncertainty; introduces the reader to the main concepts, notions and results of stochastic financial mathematics; and develops applications of these results to various kinds of calculations required in financial engineering. It also answers the requests of teachers of financial mathematics and engineering by making a bias towards probabilistic and statistical ideas and the methods of stochastic calculus in the analysis of market risks. Contents:Facts. Models:Main Concepts, Structures, and Instruments. Aims and Problems of Financial Theory and Financial EngineeringStochastic Models. Discrete TimeStochastic Models. Continuous TimeStatistical Analysis of Financial DataTheory:Theory of Arbitrage in Stochastic Financial Models. Discrete TimeTheory of Pricing in Stochastic Financial Models. Discrete TimeTheory of Arbitrage in Stochastic Financial Models. Continuous TimeTheory of Pricing in Stochastic Financial Models. Continuous Time Readership: Undergraduates and researchers in probability and statistics; applied, pure and financial mathematics; economics; chaos. Keywords:Stochastic Finance;Financial Theory;Financial Engineering;Financial MathematicsReviews: “This is a remarkable text, containing a huge amount of interesting material on modern stochastic finance. Especially the young (novice) researcher in the field will find it a very useful basis of results essential for further research. The set of references is impressive and the level of writing is clear and pedagogically sound … a much more in-depth treatment of a very wide and encompassing range of stochastic models is given. In summary: a text to be recommended warmly.” International Statistical Institute “It is a very comprehensive survey of the results from the theories of stochastic processes, time series and related statistical procedures relevant to finance applications. It also develops classical pricing models and results. It is written in a very lively style, in which the author effortlessly jumps from abstract mathematical frameworks to interesting historical remarks.” Mathematical Reviews “The author's choice of material is outstanding and well worth the time and effort it will require to get through … For anyone interested or working in the field and who have a good mathematical background, this book will be a valuable resource and a rich and stimulating source of intellectual pleasure.” Journal of Applied Mathematics and Stochastic Analysis “… as an encyclopedia of results and methods for financial analysis it is very impressive and certainly very useful as well.” Mathematics Abstracts


Basic Stochastic Processes

Filename: basic-stochastic-processes.pdf
ISBN: 9781447105336
Release Date: 2012-12-06
Number of pages: 226
Author: Zdzislaw Brzezniak
Publisher: Springer Science & Business Media

Download and read online Basic Stochastic Processes in PDF and EPUB Stochastic processes are tools used widely by statisticians and researchers working in the mathematics of finance. This book for self-study provides a detailed treatment of conditional expectation and probability, a topic that in principle belongs to probability theory, but is essential as a tool for stochastic processes. The book centers on exercises as the main means of explanation.


Probability Essentials

Filename: probability-essentials.pdf
ISBN: 9783642556821
Release Date: 2012-12-06
Number of pages: 254
Author: Jean Jacod
Publisher: Springer Science & Business Media

Download and read online Probability Essentials in PDF and EPUB This introduction can be used, at the beginning graduate level, for a one-semester course on probability theory or for self-direction without benefit of a formal course; the measure theory needed is developed in the text. It will also be useful for students and teachers in related areas such as finance theory, electrical engineering, and operations research. The text covers the essentials in a directed and lean way with 28 short chapters, and assumes only an undergraduate background in mathematics. Readers are taken right up to a knowledge of the basics of Martingale Theory, and the interested student will be ready to continue with the study of more advanced topics, such as Brownian Motion and Ito Calculus, or Statistical Inference.


Introduction to Stochastic Processes with R

Filename: introduction-to-stochastic-processes-with-r.pdf
ISBN: 9781118740651
Release Date: 2016-03-07
Number of pages: 504
Author: Robert P. Dobrow
Publisher: John Wiley & Sons

Download and read online Introduction to Stochastic Processes with R in PDF and EPUB An introduction to stochastic processes through the use of R Introduction to Stochastic Processes with R is an accessible and well-balanced presentation of the theory of stochastic processes, with an emphasis on real-world applications of probability theory in the natural and social sciences. The use of simulation, by means of the popular statistical freeware R, makes theoretical results come alive with practical, hands-on demonstrations. Written by a highly-qualified expert in the field, the author presents numerous examples from a wide array of disciplines, which are used to illustrate concepts and highlight computational and theoretical results. Developing readers’ problem-solving skills and mathematical maturity, Introduction to Stochastic Processes with R features: Over 200 examples and 600 end-of-chapter exercises A tutorial for getting started with R, and appendices that contain review material in probability and matrix algebra Discussions of many timely and interesting supplemental topics including Markov chain Monte Carlo, random walk on graphs, card shuffling, Black-Scholes options pricing, applications in biology and genetics, cryptography, martingales, and stochastic calculus Introductions to mathematics as needed in order to suit readers at many mathematical levels A companion website that includes relevant data files as well as all R code and scripts used throughout the book Introduction to Stochastic Processes with R is an ideal textbook for an introductory course in stochastic processes. The book is aimed at undergraduate and beginning graduate-level students in the science, technology, engineering, and mathematics disciplines. The book is also an excellent reference for applied mathematicians and statisticians who are interested in a review of the topic.


Stochastic Processes in Physics and Chemistry

Filename: stochastic-processes-in-physics-and-chemistry.pdf
ISBN: 0080475361
Release Date: 2011-08-30
Number of pages: 464
Author: N.G. Van Kampen
Publisher: Elsevier

Download and read online Stochastic Processes in Physics and Chemistry in PDF and EPUB The third edition of Van Kampen's standard work has been revised and updated. The main difference with the second edition is that the contrived application of the quantum master equation in section 6 of chapter XVII has been replaced with a satisfactory treatment of quantum fluctuations. Apart from that throughout the text corrections have been made and a number of references to later developments have been included. From the recent textbooks the following are the most relevant. C.W.Gardiner, Quantum Optics (Springer, Berlin 1991) D.T. Gillespie, Markov Processes (Academic Press, San Diego 1992) W.T. Coffey, Yu.P.Kalmykov, and J.T.Waldron, The Langevin Equation (2nd edition, World Scientific, 2004) * Comprehensive coverage of fluctuations and stochastic methods for describing them * A must for students and researchers in applied mathematics, physics and physical chemistry


Stochastic Processes

Filename: stochastic-processes.pdf
ISBN: 3540204822
Release Date: 2004-03-12
Number of pages: 234
Author: Kiyosi Ito
Publisher: Springer Science & Business Media

Download and read online Stochastic Processes in PDF and EPUB This introduction to the theory of stochastic processes emphasises processes with independent increments and Markov processes. Two separate Sections present about 70 exercises and their complete solutions.


Stochastic Processes for Physicists

Filename: stochastic-processes-for-physicists.pdf
ISBN: 9781139486798
Release Date: 2010-02-18
Number of pages: 204
Author: Kurt Jacobs
Publisher: Cambridge University Press

Download and read online Stochastic Processes for Physicists in PDF and EPUB Stochastic processes are an essential part of numerous branches of physics, as well as in biology, chemistry, and finance. This textbook provides a solid understanding of stochastic processes and stochastic calculus in physics, without the need for measure theory. In avoiding measure theory, this textbook gives readers the tools necessary to use stochastic methods in research with a minimum of mathematical background. Coverage of the more exotic Levy processes is included, as is a concise account of numerical methods for simulating stochastic systems driven by Gaussian noise. The book concludes with a non-technical introduction to the concepts and jargon of measure-theoretic probability theory. With over 70 exercises, this textbook is an easily accessible introduction to stochastic processes and their applications, as well as methods for numerical simulation, for graduate students and researchers in physics.


Fundamentals of Queueing Networks

Filename: fundamentals-of-queueing-networks.pdf
ISBN: 9781475753011
Release Date: 2013-04-17
Number of pages: 406
Author: Hong Chen
Publisher: Springer Science & Business Media

Download and read online Fundamentals of Queueing Networks in PDF and EPUB This accessible book aims to collect in a single volume the essentials of stochastic networks. Stochastic networks have become widely used as a basic model of many physical systems in a diverse range of fields. Written by leading authors in the field, this book is meant to be used as a reference or supplementary reading by practitioners in operations research, computer systems, communications networks, production planning, and logistics.


Life Insurance Risk Management Essentials

Filename: life-insurance-risk-management-essentials.pdf
ISBN: 3642207219
Release Date: 2011-05-04
Number of pages: 360
Author: Michael Koller
Publisher: Springer Science & Business Media

Download and read online Life Insurance Risk Management Essentials in PDF and EPUB The aim of the book is to provide an overview of risk management in life insurance companies. The focus is twofold: (1) to provide a broad view of the different topics needed for risk management and (2) to provide the necessary tools and techniques to concretely apply them in practice. Much emphasis has been put into the presentation of the book so that it presents the theory in a simple but sound manner. The first chapters deal with valuation concepts which are defined and analysed, the emphasis is on understanding the risks in corresponding assets and liabilities such as bonds, shares and also insurance liabilities. In the following chapters risk appetite and key insurance processes and their risks are presented and analysed. This more general treatment is followed by chapters describing asset risks, insurance risks and operational risks - the application of models and reporting of the corresponding risks is central. Next, the risks of insurance companies and of special insurance products are looked at. The aim is to show the intrinsic risks in some particular products and the way they can be analysed. The book finishes with emerging risks and risk management from a regulatory point of view, the standard model of Solvency II and the Swiss Solvency Test are analysed and explained. The book has several mathematical appendices which deal with the basic mathematical tools, e.g. probability theory, stochastic processes, Markov chains and a stochastic life insurance model based on Markov chains. Moreover, the appendices look at the mathematical formulation of abstract valuation concepts such as replicating portfolios, state space deflators, arbitrage free pricing and the valuation of unit linked products with guarantees. The various concepts in the book are supported by tables and figures.


An Introduction to Probability and Stochastic Processes

Filename: an-introduction-to-probability-and-stochastic-processes.pdf
ISBN: 9780486490991
Release Date: 2013
Number of pages: 403
Author: James L. Melsa
Publisher: Courier Corporation

Download and read online An Introduction to Probability and Stochastic Processes in PDF and EPUB Detailed coverage of probability theory, random variables and their functions, stochastic processes, linear system response to stochastic processes, Gaussian and Markov processes, and stochastic differential equations. 1973 edition.


Probability Statistics and Stochastic Processes

Filename: probability-statistics-and-stochastic-processes.pdf
ISBN: 9780470889749
Release Date: 2012-05-22
Number of pages: 558
Author: Peter Olofsson
Publisher: John Wiley & Sons

Download and read online Probability Statistics and Stochastic Processes in PDF and EPUB "This book provides a unique and balanced approach to probability, statistics, and stochastic processes. Readers gain a solid foundation in all three fields that serves as a stepping stone to more advanced investigations into each area. The Second Edition features new coverage of analysis of variance (ANOVA), consistency and efficiency of estimators, asymptotic theory for maximum likelihood estimators, empirical distribution function and the Kolmogorov-Smirnov test, general linear models, multiple comparisons, Markov chain Monte Carlo (MCMC), Brownian motion, martingales, and renewal theory. Many new introductory problems and exercises have also been added. This book combines a rigorous, calculus-based development of theory with a more intuitive approach that appeals to readers' sense of reason and logic, an approach developed through the author's many years of classroom experience. The book begins with three chapters that develop probability theory and introduce the axioms of probability, random variables, and joint distributions. The next two chapters introduce limit theorems and simulation. Also included is a chapter on statistical inference with a focus on Bayesian statistics, which is an important, though often neglected, topic for undergraduate-level texts. Markov chains in discrete and continuous time are also discussed within the book. More than 400 examples are interspersed throughout to help illustrate concepts and theory and to assist readers in developing an intuitive sense of the subject. Readers will find many of the examples to be both entertaining and thought provoking. This is also true for the carefully selected problems that appear at the end of each chapter"--