Probability And Stochastics

Author: Erhan Çınlar
Publisher: Springer Science & Business Media
ISBN: 9780387878591
Size: 73.80 MB
Format: PDF, ePub, Mobi
View: 6550

This text is an introduction to the modern theory and applications of probability and stochastics. The style and coverage is geared towards the theory of stochastic processes, but with some attention to the applications. In many instances the gist of the problem is introduced in practical, everyday language and then is made precise in mathematical form. The first four chapters are on probability theory: measure and integration, probability spaces, conditional expectations, and the classical limit theorems. There follows chapters on martingales, Poisson random measures, Levy Processes, Brownian motion, and Markov Processes. Special attention is paid to Poisson random measures and their roles in regulating the excursions of Brownian motion and the jumps of Levy and Markov processes. Each chapter has a large number of varied examples and exercises. The book is based on the author’s lecture notes in courses offered over the years at Princeton University. These courses attracted graduate students from engineering, economics, physics, computer sciences, and mathematics. Erhan Cinlar has received many awards for excellence in teaching, including the President’s Award for Distinguished Teaching at Princeton University. His research interests include theories of Markov processes, point processes, stochastic calculus, and stochastic flows. The book is full of insights and observations that only a lifetime researcher in probability can have, all told in a lucid yet precise style.

Probability And Stochastics

Author: Erhan Çınlar
Publisher: Springer
ISBN: 9781461428121
Size: 13.46 MB
Format: PDF, ePub, Mobi
View: 6188

This text is an introduction to the modern theory and applications of probability and stochastics. The style and coverage is geared towards the theory of stochastic processes, but with some attention to the applications. In many instances the gist of the problem is introduced in practical, everyday language and then is made precise in mathematical form. The first four chapters are on probability theory: measure and integration, probability spaces, conditional expectations, and the classical limit theorems. There follows chapters on martingales, Poisson random measures, Levy Processes, Brownian motion, and Markov Processes. Special attention is paid to Poisson random measures and their roles in regulating the excursions of Brownian motion and the jumps of Levy and Markov processes. Each chapter has a large number of varied examples and exercises. The book is based on the author’s lecture notes in courses offered over the years at Princeton University. These courses attracted graduate students from engineering, economics, physics, computer sciences, and mathematics. Erhan Cinlar has received many awards for excellence in teaching, including the President’s Award for Distinguished Teaching at Princeton University. His research interests include theories of Markov processes, point processes, stochastic calculus, and stochastic flows. The book is full of insights and observations that only a lifetime researcher in probability can have, all told in a lucid yet precise style.

Integration And Probability

Author: Paul Malliavin
Publisher: Springer Science & Business Media
ISBN: 1461242029
Size: 69.39 MB
Format: PDF
View: 6167

An introduction to analysis with the right mix of abstract theories and concrete problems. Starting with general measure theory, the book goes on to treat Borel and Radon measures and introduces the reader to Fourier analysis in Euclidean spaces with a treatment of Sobolev spaces, distributions, and the corresponding Fourier analysis. It continues with a Hilbertian treatment of the basic laws of probability including Doob's martingale convergence theorem and finishes with Malliavin's "stochastic calculus of variations" developed in the context of Gaussian measure spaces. This invaluable contribution gives a taste of the fact that analysis is not a collection of independent theories, but can be treated as a whole.

Brownian Motion And Stochastic Calculus

Author: Ioannis Karatzas
Publisher: Springer
ISBN: 1461209498
Size: 69.88 MB
Format: PDF, Docs
View: 389

A graduate-course text, written for readers familiar with measure-theoretic probability and discrete-time processes, wishing to explore stochastic processes in continuous time. The vehicle chosen for this exposition is Brownian motion, which is presented as the canonical example of both a martingale and a Markov process with continuous paths. In this context, the theory of stochastic integration and stochastic calculus is developed, illustrated by results concerning representations of martingales and change of measure on Wiener space, which in turn permit a presentation of recent advances in financial economics. The book contains a detailed discussion of weak and strong solutions of stochastic differential equations and a study of local time for semimartingales, with special emphasis on the theory of Brownian local time. The whole is backed by a large number of problems and exercises.

Probability 1

Author: Albert N. Shiryaev
Publisher: Springer
ISBN: 0387722068
Size: 35.74 MB
Format: PDF, ePub, Mobi
View: 3211

Advanced maths students have been waiting for this, the third edition of a text that deals with one of the fundamentals of their field. This book contains a systematic treatment of probability from the ground up, starting with intuitive ideas and gradually developing more sophisticated subjects, such as random walks and the Kalman-Bucy filter. Examples are discussed in detail, and there are a large number of exercises. This third edition contains new problems and exercises, new proofs, expanded material on financial mathematics, financial engineering, and mathematical statistics, and a final chapter on the history of probability theory.

Functional Analysis For Probability And Stochastic Processes

Author: Adam Bobrowski
Publisher: Cambridge University Press
ISBN: 9780521831666
Size: 30.92 MB
Format: PDF, ePub
View: 6437

This text is designed both for students of probability and stochastic processes, and for students of functional analysis. It presents some chosen parts of functional analysis that can help understand ideas from probability and stochastic processes. The subjects range from basic Hilbert and Banach spaces, through weak topologies and Banach algebras, to the theory of semigroups of bounded linear operators. Numerous standard and non-standard examples and exercises make the book suitable as a course textbook as well as for self-study.

Probability Theory Ii

Author: M. Loeve
Publisher: Springer Science & Business Media
ISBN: 9780387902623
Size: 31.27 MB
Format: PDF, ePub
View: 4109

This book is intended as a text for graduate students and as a reference for workers in probability and statistics. The prerequisite is honest calculus. The material covered in Parts Two to Five inclusive requires about three to four semesters of graduate study. The introductory part may serve as a text for an undergraduate course in elementary probability theory. Numerous historical marks about results, methods, and the evolution of various fields are an intrinsic part of the text. About a third of the second volume is devoted to conditioning and properties of sequences of various types of dependence. The other two thirds are devoted to random functions; the last Part on Elements of random analysis is more sophisticated.

Brownian Motion Martingales And Stochastic Calculus

Author: Jean-François Le Gall
Publisher: Springer
ISBN: 3319310895
Size: 48.82 MB
Format: PDF, ePub, Docs
View: 5952

This book offers a rigorous and self-contained presentation of stochastic integration and stochastic calculus within the general framework of continuous semimartingales. The main tools of stochastic calculus, including Itô’s formula, the optional stopping theorem and Girsanov’s theorem, are treated in detail alongside many illustrative examples. The book also contains an introduction to Markov processes, with applications to solutions of stochastic differential equations and to connections between Brownian motion and partial differential equations. The theory of local times of semimartingales is discussed in the last chapter. Since its invention by Itô, stochastic calculus has proven to be one of the most important techniques of modern probability theory, and has been used in the most recent theoretical advances as well as in applications to other fields such as mathematical finance. Brownian Motion, Martingales, and Stochastic Calculus provides a strong theoretical background to the reader interested in such developments. Beginning graduate or advanced undergraduate students will benefit from this detailed approach to an essential area of probability theory. The emphasis is on concise and efficient presentation, without any concession to mathematical rigor. The material has been taught by the author for several years in graduate courses at two of the most prestigious French universities. The fact that proofs are given with full details makes the book particularly suitable for self-study. The numerous exercises help the reader to get acquainted with the tools of stochastic calculus.

Essentials Of Stochastic Finance

Author: Albert N Shiryaev
Publisher: World Scientific
ISBN: 9814495662
Size: 41.93 MB
Format: PDF, ePub
View: 7415

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