Download or read book Stratonovich Stochastic Differential Equations Driven by General Semimartingales written by T. G. Kurtz and published by . This book was released on 1991 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Stochastic Integration and Differential Equations written by Philip E. Protter and published by Springer Verlag. This book was released on 1990 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is quite different from others on the subject in that it presents a rapid introduction to the modern semimartingale theory of stochastic integration and differential equations, without first having to treat the beautiful but highly technical "general theory of processes". The author's new approach (based on the theorem of Bitcheler-Dellacherie) also give a more intuitive understanding of the subject, and permits proofs to be much less technical. All of the major theorems of stochastic integration are given, including a comprehensive treatment (first time in English) of local times. A theory of stochastic differential equations driven by semimartingales is developed, including Fisk-Stratonovich equations, Markov properties, stability, and an introduction to the theory of flows. Further topics presented for the 1st time in book form include an elementary presentation of Azema's martingale. This book will quickly become a standard reference on the subject, to be used by specialists and non-specialists alike, both for the sake of the theory and for its application.

Download or read book Stability of Stochastic Differential Equations Driven by General Semimartingales written by Leszek Słomiński and published by . This book was released on 1996 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Stability of Stochastic Differential Equations Driven by General Semimartingales written by Leszek Slomiński and published by . This book was released on 1996 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Approximations of Stochastic Equations Driven by Predictable Processes written by Guillermo Ferreyra and published by . This book was released on 1987 with total page 13 pages. Available in PDF, EPUB and Kindle. Book excerpt: A theory of stochastic integral equations driven by predictable processes in Stratonovich sense is developed. These driving processes include a large class of discontinuous semimartingales. The theory of stochastic differential equations driven by continuous semimartingales in Stratonovich sense is extended without involving Lebesgue-Stieltjes integrals as done by Meyer. Moreover, a change of variables formula without extra terms involving the jumps of the processes holds for this theory. Results on approximation of driving processes are preserved.

Download or read book Stochastic Integration and Differential Equations written by Philip Protter and published by Springer. This book was released on 2013-12-21 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Emery’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.

Download or read book General Stochastic Measures written by Vadym M. Radchenko and published by John Wiley & Sons. This book was released on 2022-08-23 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the study of stochastic measures (SMs). An SM is a sigma-additive in probability random function, defined on a sigma-algebra of sets. SMs can be generated by the increments of random processes from many important classes such as square-integrable martingales and fractional Brownian motion, as well as alpha-stable processes. SMs include many well-known stochastic integrators as partial cases. General Stochastic Measures provides a comprehensive theoretical overview of SMs, including the basic properties of the integrals of real functions with respect to SMs. A number of results concerning the Besov regularity of SMs are presented, along with equations driven by SMs, types of solution approximation and the averaging principle. Integrals in the Hilbert space and symmetric integrals of random functions are also addressed. The results from this book are applicable to a wide range of stochastic processes, making it a useful reference text for researchers and postgraduate or postdoctoral students who specialize in stochastic analysis.

Download or read book Stochastic Ordinary and Stochastic Partial Differential Equations written by Peter Kotelenez and published by Springer Science & Business Media. This book was released on 2007-12-05 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic Partial Differential Equations analyzes mathematical models of time-dependent physical phenomena on microscopic, macroscopic and mesoscopic levels. It provides a rigorous derivation of each level from the preceding one and examines the resulting mesoscopic equations in detail. Coverage first describes the transition from the microscopic equations to the mesoscopic equations. It then covers a general system for the positions of the large particles.

Download or read book Stochastic Differential Equations written by Bernt Oksendal and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews to the first edition: Most of the literature about stochastic differential equations seems to place so much emphasis on rigor and completeness that it scares the nonexperts away. These notes are an attempt to approach the subject from the nonexpert point of view.: Not knowing anything ... about a subject to start with, what would I like to know first of all. My answer would be: 1) In what situations does the subject arise ? 2) What are its essential features? 3) What are the applications and the connections to other fields?" The author, a lucid mind with a fine pedagocical instinct, has written a splendid text that achieves his aims set forward above. He starts out by stating six problems in the introduction in which stochastic differential equations play an essential role in the solution. Then, while developing stochastic calculus, he frequently returns to these problems and variants thereof and to many other problems to show how thetheory works and to motivate the next step in the theoretical development. Needless to say, he restricts himself to stochastic integration with respectto Brownian motion. He is not hesitant to give some basic results without proof in order to leave room for "some more basic applications"... It can be an ideal text for a graduate course, but it is also recommended to analysts (in particular, those working in differential equations and deterministic dynamical systems and control) who wish to learn quickly what stochastic differential equations are all about. From: Acta Scientiarum Mathematicarum, Tom 50, 3-4, 1986

Download or read book Stochastic Processes and Applications to Mathematical Finance written by Jiro Akahori and published by World Scientific. This book was released on 2004 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains articles on stochastic processes (stochastic calculus and Malliavin calculus, functionals of Brownian motions and Levy processes, stochastic control and optimization problems, stochastic numerics, and so on) and their applications to problems in mathematical finance. Examples of topics are applications of Malliavin calculus and numerical analysis to a new simulation scheme for calculating the price of financial derivatives, applications of the asymptotic expansion method in Malliavin calculus to financial problems, semimartingale decompositions under an enlargement of filtrations in connection with insider problems, and the problem of transaction costs in connection with stochastic control and optimization problems.

Download or read book Approximations of Solutions of Stochastic Differential Equations Driven by Semimartingales written by P. Protter and published by . This book was released on 1983 with total page 45 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Seminaire de Probabilites XXXI written by Jacques Azema and published by Springer. This book was released on 2008-05-01 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 31 papers collected here present original research results obtained in 1995-96, on Brownian motion and, more generally, diffusion processes, martingales, Wiener spaces, polymer measures.

Download or read book A Course on Rough Paths written by Peter K. Friz and published by Springer Nature. This book was released on 2020-05-27 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: With many updates and additional exercises, the second edition of this book continues to provide readers with a gentle introduction to rough path analysis and regularity structures, theories that have yielded many new insights into the analysis of stochastic differential equations, and, most recently, stochastic partial differential equations. Rough path analysis provides the means for constructing a pathwise solution theory for stochastic differential equations which, in many respects, behaves like the theory of deterministic differential equations and permits a clean break between analytical and probabilistic arguments. Together with the theory of regularity structures, it forms a robust toolbox, allowing the recovery of many classical results without having to rely on specific probabilistic properties such as adaptedness or the martingale property. Essentially self-contained, this textbook puts the emphasis on ideas and short arguments, rather than aiming for the strongest possible statements. A typical reader will have been exposed to upper undergraduate analysis and probability courses, with little more than Itô-integration against Brownian motion required for most of the text. From the reviews of the first edition: "Can easily be used as a support for a graduate course ... Presents in an accessible way the unique point of view of two experts who themselves have largely contributed to the theory" - Fabrice Baudouin in the Mathematical Reviews "It is easy to base a graduate course on rough paths on this ... A researcher who carefully works her way through all of the exercises will have a very good impression of the current state of the art" - Nicolas Perkowski in Zentralblatt MATH

Download or read book Stochastic Processes And Applications To Mathematical Finance Proceedings Of The Ritsumeikan International Symposium written by Jiro Akahori and published by World Scientific. This book was released on 2004-07-06 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains 17 articles on stochastic processes (stochastic calculus and Malliavin calculus, functionals of Brownian motions and Lévy processes, stochastic control and optimization problems, stochastic numerics, and so on) and their applications to problems in mathematical finance.The proceedings have been selected for coverage in:• Index to Scientific & Technical Proceedings® (ISTP® / ISI Proceedings)• Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)• Index to Social Sciences & Humanities Proceedings® (ISSHP® / ISI Proceedings)• Index to Social Sciences & Humanities Proceedings (ISSHP CDROM version / ISI Proceedings)• CC Proceedings — Engineering & Physical Sciences

Download or read book Stochastic Processes and Applications to Mathematical Finance written by and published by World Scientific. This book was released on 2004 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains 17 articles on stochastic processes (stochastic calculus and Malliavin calculus, functionals of Brownian motions and L(r)vy processes, stochastic control and optimization problems, stochastic numerics, and so on) and their applications to problems in mathematical finance.The proceedings have been selected for coverage in: OCo Index to Scientific & Technical Proceedings- (ISTP- / ISI Proceedings)OCo Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)OCo Index to Social Sciences & Humanities Proceedings- (ISSHP- / ISI Proceedings)OCo Index to Social Sciences & Humanities Proceedings (ISSHP CDROM version / ISI Proceedings)OCo CC Proceedings OCo Engineering & Physical Sciences"

Download or read book Stochastic Analysis and Applications in Physics written by Ana Isabel Cardoso and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the NATO Advanced Study Institute, Funchal, Madeira, Portugal, August 6--19, 1993

Download or read book Stochastic Analysis and Related Topics VI written by Laurent Decreusefond and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the contributions of the participants of the Sixth Oslo-Silivri Workshop on Stochastic Analysis, held in Geilo from July 29 to August 6, 1996. There are two main lectures " Stochastic Differential Equations with Memory, by S.E.A. Mohammed, " Backward SDE's and Viscosity Solutions of Second Order Semilinear PDE's, by E. Pardoux. The main lectures are presented at the beginning of the volume. There is also a review paper at the third place about the stochastic calculus of variations on Lie groups. The contributing papers vary from SPDEs to Non-Kolmogorov type probabilistic models. We would like to thank " VISTA, a research cooperation between Norwegian Academy of Sciences and Letters and Den Norske Stats Oljeselskap (Statoil), " CNRS, Centre National de la Recherche Scientifique, " The Department of Mathematics of the University of Oslo, " The Ecole Nationale Superieure des Telecommunications, for their financial support. L. Decreusefond J. Gjerde B. 0ksendal A.S. Ustunel PARTICIPANTS TO THE 6TH WORKSHOP ON STOCHASTIC ANALYSIS Vestlia HØyfjellshotell, Geilo, Norway, July 28 -August 4, 1996. E-mail: [email protected] Aureli ALABERT Departament de Matematiques Laurent DECREUSEFOND Universitat Autonoma de Barcelona Ecole Nationale Superieure des Telecom 08193-Bellaterra munications CATALONIA (Spain) Departement Reseaux E-mail: [email protected] 46, rue Barrault Halvard ARNTZEN 75634 Paris Cedex 13 Dept. of Mathematics FRANCE University of Oslo E-mail: [email protected] Box 1053 Blindern Laurent DENIS N-0316 Oslo C.M.I