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Ordinary differential equations --- Stochastic processes --- Differentiaalvergelijkingen [Stochastische ] --- Equations differentielles stochastiques --- Integralen [Stochastische ] --- Integrales stochastiques --- Integrals [Stochastic ] --- Martingalen (Wiskunde) --- Martingales (Mathematics) --- Martingales (Mathematiques) --- Stochastic differential equations --- Stochastic integrals --- Martingales (Mathématiques) --- Equations différentielles stochastiques --- 519.217 --- Markov processes --- 519.217 Markov processes --- Martingales (Mathématiques) --- Equations différentielles stochastiques --- Differential equations --- Fokker-Planck equation --- Integrals, Stochastic --- Stochastic analysis
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It has been 15 years since the first edition of Stochastic Integration and Differential Equations, A New Approach appeared, and in those years many other texts on the same subject have been published, often with connections to applications, especially mathematical finance. Yet in spite of the apparent simplicity of approach, none of these books has used the functional analytic method of presenting semimartingales and stochastic integration. Thus a 2nd edition seems worthwhile and timely, though it is no longer appropriate to call it "a new approach". The new edition has several significant changes, most prominently the addition of exercises for solution. These are intended to supplement the text, but lemmas needed in a proof are never relegated to the exercises. Many of the exercises have been tested by graduate students at Purdue and Cornell Universities. Chapter 3 has been completely redone, with a new, more intuitive and simultaneously elementary proof of the fundamental Doob-Meyer decomposition theorem, the more general version of the Girsanov theorem due to Lenglart, the Kazamaki-Novikov criteria for exponential local martingales to be martingales, and a modern treatment of compensators. Chapter 4 treats sigma martingales (important in finance theory) and gives a more comprehensive treatment of martingale representation, including both the Jacod-Yor theory and Emeryâ¬(tm)s examples of martingales that actually have martingale representation (thus going beyond the standard cases of Brownian motion and the compensated Poisson process). New topics added include an introduction to the theory of the expansion of filtrations, a treatment of the Fefferman martingale inequality, and that the dual space of the martingale space H^1 can be identified with BMO martingales. Solutions to selected exercises are available at the web site of the author, with current URL http://www.orie.cornell.edu/~protter/books.html.
Martingales (Mathematics) --- Stochastic differential equations --- Stochastic differential equations. --- Stochastic integrals. --- Martingales (Mathematics). --- Stochastic integrals --- Integrals, Stochastic --- Ordinary differential equations --- Stochastic processes --- 519.2 --- 305.91 --- AA / International- internationaal --- Differential equations --- Fokker-Planck equation --- Stochastic analysis --- Econometrie van de financiële activa. Portfolio allocation en management. CAPM. Bubbles --- Probabilities. --- Mathematical analysis. --- Analysis (Mathematics). --- Partial differential equations. --- Applied mathematics. --- Engineering mathematics. --- Probability Theory and Stochastic Processes. --- Analysis. --- Partial Differential Equations. --- Mathematical and Computational Engineering. --- Engineering --- Engineering analysis --- Mathematical analysis --- Partial differential equations --- 517.1 Mathematical analysis --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Anàlisi estocàstica --- Anàlisi matemàtica --- Processos estocàstics --- Càlcul de Malliavin --- Equacions integrals estocàstiques --- Integrals estocàstiques
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In applications, and especially in mathematical finance, random time-dependent events are often modeled as stochastic processes. Assumptions are made about the structure of such processes, and serious researchers will want to justify those assumptions through the use of data. As statisticians are wont to say, “In God we trust; all others must bring data.” This book establishes the theory of how to go about estimating not just scalar parameters about a proposed model, but also the underlying structure of the model itself. Classic statistical tools are used: the law of large numbers, and the central limit theorem. Researchers have recently developed creative and original methods to use these tools in sophisticated (but highly technical) ways to reveal new details about the underlying structure. For the first time in book form, the authors present these latest techniques, based on research from the last 10 years. They include new findings. This book will be of special interest to researchers, combining the theory of mathematical finance with its investigation using market data, and it will also prove to be useful in a broad range of applications, such as to mathematical biology, chemical engineering, and physics.
Stochastic analysis. --- Discretization (Mathematics) --- Civil & Environmental Engineering --- Mathematics --- Engineering & Applied Sciences --- Physical Sciences & Mathematics --- Mathematical Statistics --- Operations Research --- Stochastic processes. --- Random processes --- Mathematics. --- Probabilities. --- Statistics. --- Econometrics. --- Probability Theory and Stochastic Processes. --- Statistics for Business/Economics/Mathematical Finance/Insurance. --- Probabilities --- Distribution (Probability theory. --- Statistics for Business, Management, Economics, Finance, Insurance. --- Economics, Mathematical --- Statistics --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Econometrics --- Distribution functions --- Frequency distribution --- Characteristic functions --- Statistics . --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk
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We present here a one-semester course on Probability Theory. We also treat measure theory and Lebesgue integration, concentrating on those aspects which are especially germane to the study of Probability Theory. The book is intended to fill a current need: there are mathematically sophisticated stu dents and researchers (especially in Engineering, Economics, and Statistics) who need a proper grounding in Probability in order to pursue their primary interests. Many Probability texts available today are celebrations of Prob ability Theory, containing treatments of fascinating topics to be sure, but nevertheless they make it difficult to construct a lean one semester course that covers (what we believe are) the essential topics. Chapters 1-23 provide such a course. We have indulged ourselves a bit by including Chapters 24-28 which are highly optional, but which may prove useful to Economists and Electrical Engineers. This book had its origins in a course the second author gave in Perugia, Italy, in 1997; he used the samizdat "notes" of the first author, long used for courses at the University of Paris VI, augmenting them as needed. The result has been further tested at courses given at Purdue University. We thank the indulgence and patience of the students both in Perugia and in West Lafayette. We also thank our editor Catriona Byrne, as weil as Nick Bingham for many superb suggestions, an anonymaus referee for the same, and Judy Mitchell for her extraordinary typing skills. Jean Jacod, Paris Philip Protter, West Lafayette Contents 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . . . . . . .
Probabilities. --- AA / International- internationaal --- 303.3 --- Waarschijnlijkheid. Probabiliteit. Nauwkeurigheid. Residuals: measurement and specification (wiskundige statistiek). --- Probabilités --- Probabilities --- Probability --- Statistical inference --- Waarschijnlijkheid. Probabiliteit. Nauwkeurigheid. Residuals: measurement and specification (wiskundige statistiek) --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Probability Theory and Stochastic Processes.
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Quantitative methods (economics) --- Operational research. Game theory --- Mathematical statistics --- Business economics --- stochastische analyse --- statistiek --- econometrie --- kansrekening
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This introduction to Probability Theory 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 (Economics), Electrical Engineering, and Operations Research. The text covers the essentials in a directed and lean way with 28 short chapters. Assuming of readers only an undergraduate background in mathematics, it brings them from a starting knowledge of the subject to a knowledge of the basics of Martingale Theory. After learning Probability Theory from this text, 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. The second edition contains some additions to the text and to the references and some parts are completely rewritten.
Probabilities --- Probabilities. --- Economics, Mathematical . --- Probability Theory and Stochastic Processes. --- Quantitative Finance. --- Economics --- Mathematical economics --- Econometrics --- Mathematics --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Methodology --- Probabilités. --- Probabilités --- Processus stochastiques --- Martingales
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In applications, and especially in mathematical finance, random time-dependent events are often modeled as stochastic processes. Assumptions are made about the structure of such processes, and serious researchers will want to justify those assumptions through the use of data. As statisticians are wont to say, In God we trust; all others must bring data. This book establishes the theory of how to go about estimating not just scalar parameters about a proposed model, but also the underlying structure of the model itself. Classic statistical tools are used: the law of large numbers, and the central limit theorem. Researchers have recently developed creative and original methods to use these tools in sophisticated (but highly technical) ways to reveal new details about the underlying structure. For the first time in book form, the authors present these latest techniques, based on research from the last 10 years. They include new findings. This book will be of special interest to researchers, combining the theory of mathematical finance with its investigation using market data, and it will also prove to be useful in a broad range of applications, such as to mathematical biology, chemical engineering, and physics.
Quantitative methods (economics) --- Operational research. Game theory --- Mathematical statistics --- Business economics --- stochastische analyse --- statistiek --- econometrie --- kansrekening
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The current volume presents four chapters touching on some of the most important and modern areas of research in Mathematical Finance: asset price bubbles (by Philip Protter); energy markets (by Fred Espen Benth); investment under transaction costs (by Paolo Guasoni and Johannes Muhle-Karbe); and numerical methods for solving stochastic equations (by Dan Crisan, K. Manolarakis and C. Nee).The Paris-Princeton Lecture Notes on Mathematical Finance, of which this is the fifth volume, publish cutting-edge research in self-contained, expository articles from renowned specialists. The aim is to produce a series of articles that can serve as an introductory reference source for research in the field.
Finance --- Economics --- Mathematics --- Operational research. Game theory --- financieel management --- economie --- speltheorie --- wiskunde
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