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 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 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 Stability of Stochastic Differential Equations with Respect to Semimartingales written by Xuerong Mao and published by . This book was released on 1991 with total page 300 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 Stochastic Stability of Differential Equations written by Rafail Khasminskii and published by Springer Science & Business Media. This book was released on 2011-09-20 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the publication of the first edition of the present volume in 1980, the stochastic stability of differential equations has become a very popular subject of research in mathematics and engineering. To date exact formulas for the Lyapunov exponent, the criteria for the moment and almost sure stability, and for the existence of stationary and periodic solutions of stochastic differential equations have been widely used in the literature. In this updated volume readers will find important new results on the moment Lyapunov exponent, stability index and some other fields, obtained after publication of the first edition, and a significantly expanded bibliography. This volume provides a solid foundation for students in graduate courses in mathematics and its applications. It is also useful for those researchers who would like to learn more about this subject, to start their research in this area or to study the properties of concrete mechanical systems subjected to random perturbations.

Download or read book Reflecting Stochastic Differential Equations with Jumps and Applications written by Situ Rong and published by CRC Press. This book was released on 1999-08-05 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many important physical variables satisfy certain dynamic evolution systems and can take only non-negative values. Therefore, one can study such variables by studying these dynamic systems. One can put some conditions on the coefficients to ensure non-negative values in deterministic cases. However, as a random process disturbs the system, the components of solutions to stochastic differential equations (SDE) can keep changing between arbitrary large positive and negative values-even in the simplest case. To overcome this difficulty, the author examines the reflecting stochastic differential equation (RSDE) with the coordinate planes as its boundary-or with a more general boundary. Reflecting Stochastic Differential Equations with Jumps and Applications systematically studies the general theory and applications of these equations. In particular, the author examines the existence, uniqueness, comparison, convergence, and stability of strong solutions to cases where the RSDE has discontinuous coefficients-with greater than linear growth-that may include jump reflection. He derives the nonlinear filtering and Zakai equations, the Maximum Principle for stochastic optimal control, and the necessary and sufficient conditions for the existence of optimal control. Most of the material presented in this book is new, including much new work by the author concerning SDEs both with and without reflection. Much of it appears here for the first time. With the application of RSDEs to various real-life problems, such as the stochastic population and neurophysiological control problems-both addressed in the text-scientists dealing with stochastic dynamic systems will find this an interesting and useful work.

Download or read book Stability of Infinite Dimensional Stochastic Differential Equations with Applications written by Kai Liu and published by CRC Press. This book was released on 2005-08-23 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic differential equations in infinite dimensional spaces are motivated by the theory and analysis of stochastic processes and by applications such as stochastic control, population biology, and turbulence, where the analysis and control of such systems involves investigating their stability. While the theory of such equations is well establ

Download or read book Stochastic Differential Equations and Applications written by X Mao and published by Elsevier. This book was released on 2007-12-30 with total page 445 pages. Available in PDF, EPUB and Kindle. Book excerpt: This advanced undergraduate and graduate text has now been revised and updated to cover the basic principles and applications of various types of stochastic systems, with much on theory and applications not previously available in book form. The text is also useful as a reference source for pure and applied mathematicians, statisticians and probabilists, engineers in control and communications, and information scientists, physicists and economists. Has been revised and updated to cover the basic principles and applications of various types of stochastic systems Useful as a reference source for pure and applied mathematicians, statisticians and probabilists, engineers in control and communications, and information scientists, physicists and economists

Download or read book Stochastic Differential Equations Driven by Levy Processes written by Changyong Zhang and published by LAP Lambert Academic Publishing. This book was released on 2011-12 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic differential equations driven by Levy processes are used as mathematical models for random dynamic phenomena in applications arising from fields such as finance and insurance, to capture continuous and discontinuous uncertainty. For many applications, a stochastic differential equation does not have a closed-form solution and the weak Euler approximation is applied. In such numerical treatment of stochastic differential equations, it is of theoretical and practical importance to estimate the rate of convergence of the discrete time approximation. In this book, it is systematically investigated the dependence of the rate of convergence on the regularity of the coefficients and driving processes. The model under consideration is of a more general form than existing ones, and hence is applicable to a broader range of processes, from the widely-studied diffusions and stochastic differential equations driven by spherically-symmetric stable processes to stochastic differential equations driven by more general Levy processes. These processes can be found in a variety of fields, including physics, engineering, economics, and finance.

Download or read book Stability of Solutions of Stochastic Differential Equations of Diffusion Type written by Piotr Szlenk and published by . This book was released on 1993 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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 Stochastic Stability of Differential Equations in Abstract Spaces written by Kai Liu and published by Cambridge University Press. This book was released on 2019-05-02 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: The stability of stochastic differential equations in abstract, mainly Hilbert, spaces receives a unified treatment in this self-contained book. It covers basic theory as well as computational techniques for handling the stochastic stability of systems from mathematical, physical and biological problems. Its core material is divided into three parts devoted respectively to the stochastic stability of linear systems, non-linear systems, and time-delay systems. The focus is on stability of stochastic dynamical processes affected by white noise, which are described by partial differential equations such as the Navier–Stokes equations. A range of mathematicians and scientists, including those involved in numerical computation, will find this book useful. It is also ideal for engineers working on stochastic systems and their control, and researchers in mathematical physics or biology.

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 2006 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based around recent lectures given at the prestigious Ritsumeikan conference, the tutorial and expository articles contained in this volume are an essential guide for practitioners and graduates alike who use stochastic calculus in finance.Among the eminent contributors are Paul Malliavin and Shinzo Watanabe, pioneers of Malliavin Calculus. The coverage also includes a valuable review of current research on credit risks in a mathematically sophisticated way contrasting with existing economics-oriented articles.

Download or read book Exponential Stability of Stochastic Differential Equations written by Xuerong Mao and published by CRC Press. This book was released on 1994-05-02 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work presents a systematic study of current developments in stochastic differential delay equations driven by nonlinear integrators, detailing various exponential stabilities for stochastic differential equations and large-scale systems. It illustrates the practical use of stochastic stabilization, stochastic destabilization, stochastic flows, and stochastic oscillators in numerous real-world situations.

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 Stochastic Equations in Infinite Dimensions written by Giuseppe Da Prato and published by Cambridge University Press. This book was released on 2014-04-17 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt: Now in its second edition, this book gives a systematic and self-contained presentation of basic results on stochastic evolution equations in infinite dimensional, typically Hilbert and Banach, spaces. In the first part the authors give a self-contained exposition of the basic properties of probability measure on separable Banach and Hilbert spaces, as required later; they assume a reasonable background in probability theory and finite dimensional stochastic processes. The second part is devoted to the existence and uniqueness of solutions of a general stochastic evolution equation, and the third concerns the qualitative properties of those solutions. Appendices gather together background results from analysis that are otherwise hard to find under one roof. This revised edition includes two brand new chapters surveying recent developments in the area and an even more comprehensive bibliography, making this book an essential and up-to-date resource for all those working in stochastic differential equations.