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Reflecting Stochastic Differential Equations With Jumps And Applications
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Book Synopsis Reflecting Stochastic Differential Equations with Jumps and Applications by : Situ Rong
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.
Book Synopsis Theory of Stochastic Differential Equations with Jumps and Applications by : Rong SITU
Download or read book Theory of Stochastic Differential Equations with Jumps and Applications written by Rong SITU and published by Springer Science & Business Media. This book was released on 2006-05-06 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic differential equations (SDEs) are a powerful tool in science, mathematics, economics and finance. This book will help the reader to master the basic theory and learn some applications of SDEs. In particular, the reader will be provided with the backward SDE technique for use in research when considering financial problems in the market, and with the reflecting SDE technique to enable study of optimal stochastic population control problems. These two techniques are powerful and efficient, and can also be applied to research in many other problems in nature, science and elsewhere.
Book Synopsis Backward Stochastic Differential Equations with Jumps and Applications by : Rong Situ
Download or read book Backward Stochastic Differential Equations with Jumps and Applications written by Rong Situ and published by . This book was released on 2000 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Backward Stochastic Differential Equations with Jumps and Their Actuarial and Financial Applications by : Łukasz Delong
Download or read book Backward Stochastic Differential Equations with Jumps and Their Actuarial and Financial Applications written by Łukasz Delong and published by Springer Science & Business Media. This book was released on 2013-06-12 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: Backward stochastic differential equations with jumps can be used to solve problems in both finance and insurance. Part I of this book presents the theory of BSDEs with Lipschitz generators driven by a Brownian motion and a compensated random measure, with an emphasis on those generated by step processes and Lévy processes. It discusses key results and techniques (including numerical algorithms) for BSDEs with jumps and studies filtration-consistent nonlinear expectations and g-expectations. Part I also focuses on the mathematical tools and proofs which are crucial for understanding the theory. Part II investigates actuarial and financial applications of BSDEs with jumps. It considers a general financial and insurance model and deals with pricing and hedging of insurance equity-linked claims and asset-liability management problems. It additionally investigates perfect hedging, superhedging, quadratic optimization, utility maximization, indifference pricing, ambiguity risk minimization, no-good-deal pricing and dynamic risk measures. Part III presents some other useful classes of BSDEs and their applications. This book will make BSDEs more accessible to those who are interested in applying these equations to actuarial and financial problems. It will be beneficial to students and researchers in mathematical finance, risk measures, portfolio optimization as well as actuarial practitioners.
Book Synopsis An Introduction to Stochastic Differential Equations with Reflection by : Andrey Pilipenko
Download or read book An Introduction to Stochastic Differential Equations with Reflection written by Andrey Pilipenko and published by Universitätsverlag Potsdam. This book was released on 2014 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Abstract and Applied Analysis by : N. M. Chuong
Download or read book Abstract and Applied Analysis written by N. M. Chuong and published by World Scientific. This book was released on 2004 with total page 579 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume takes up various topics in Mathematical Analysis including boundary and initial value problems for Partial Differential Equations and Functional Analytic methods. Topics include linear elliptic systems for composite material OCo the coefficients may jump from domain to domain; Stochastic Analysis OCo many applied problems involve evolution equations with random terms, leading to the use of stochastic analysis. The proceedings have been selected for coverage in: . OCo Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings). OCo CC Proceedings OCo Engineering & Physical Sciences. Contents: Deterministic Analysis: Differentiation of Hypergeometric Functions with Respect to Parameters (Yu A Brychkov & K O Geddes); On the Lagrange Problem About the Strongest Columns (Yu V Egorov); Wavelet Based Fast Solution of Boundary Integral Equations (H Harbrecht & R Schneider); Semi-Classical Methods in GinzburgOCoLandau Theory (B Helffer); Stability of Equilibriums in One-Dimensional Motion of Compressible Viscous Gas Forced by Self-Gravity (Y Iwata & Y Yamamoto); Estimates for Elliptic Systems for Composite Material (L Nirenberg); On Asymptotics for the Mabuchi Energy Functional (D H Phong & J Sturm); Regularity of Solutions of the Initial Boundary Value Problem for Linearized Equations of Ideal Magneto-Hydrodynamics (M Yamamoto); Stochastic Analysis: Impulsive Stochastic Evolution Inclusions with Multi-Valued Diffusion (N U Ahmed); Some of Future Directions of White Noise Analysis (T Hida); Constructing Random Probability Distributions (T P Hill & D E R Sitton); Multiparameter Additive Processes of Mixture Type (K Inoue); The Random Integral Representation Hypothesis Revisited: New Classes of S-Selfdecomposable Laws (Z J Jurek); Semigroups and Processes with Parameter in a Cone (J Pedersen & K-I Sato); and other papers. Readership: Researchers and academics in the fields of analysis and differential equations, approximation theory, probability and statistics."
Book Synopsis Stochastic Partial Differential Equations and Applications by : Giuseppe Da Prato
Download or read book Stochastic Partial Differential Equations and Applications written by Giuseppe Da Prato and published by CRC Press. This book was released on 2002-04-05 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on the proceedings of the International Conference on Stochastic Partial Differential Equations and Applications-V held in Trento, Italy, this illuminating reference presents applications in filtering theory, stochastic quantization, quantum probability, and mathematical finance and identifies paths for future research in the field. Stochastic Partial Differential Equations and Applications analyzes recent developments in the study of quantum random fields, control theory, white noise, and fluid dynamics. It presents precise conditions for nontrivial and well-defined scattering, new Gaussian noise terms, models depicting the asymptotic behavior of evolution equations, and solutions to filtering dilemmas in signal processing. With contributions from more than 40 leading experts in the field, Stochastic Partial Differential Equations and Applications is an excellent resource for pure and applied mathematicians; numerical analysts; mathematical physicists; geometers; economists; probabilists; computer scientists; control, electrical, and electronics engineers; and upper-level undergraduate and graduate students in these disciplines.
Book Synopsis Stochastic Differential Equations by : Bernt Oksendal
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 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "The author, a lucid mind with a fine pedagogical instinct, has written a splendid text. 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 the theory works and to motivate the next step in the theoretical development. Needless to say, he restricts himself to stochastic integration with respect to Brownian motion. He is not hesitant to give some basic results without proof in order to leave room for "some more basic applications... The book 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." Acta Scientiarum Mathematicarum, Tom 50, 3-4, 1986#1 "The book is well written, gives a lot of nice applications of stochastic differential equation theory, and presents theory and applications of stochastic differential equations in a way which makes the book useful for mathematical seminars at a low level. (...) The book (will) really motivate scientists from non-mathematical fields to try to understand the usefulness of stochastic differential equations in their fields." Metrica#2
Book Synopsis Stochastic Integration with Jumps by : Klaus Bichteler
Download or read book Stochastic Integration with Jumps written by Klaus Bichteler and published by Cambridge University Press. This book was released on 2002-05-13 with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt: The complete theory of stochastic differential equations driven by jumps, their stability, and numerical approximation theories.
Book Synopsis Proceedings of the International Conference on Stochastic Analysis and Applications by : Sergio Albeverio
Download or read book Proceedings of the International Conference on Stochastic Analysis and Applications written by Sergio Albeverio and published by Springer Science & Business Media. This book was released on 2013-03-20 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic analysis is a field of mathematical research having numerous interactions with other domains of mathematics such as partial differential equations, riemannian path spaces, dynamical systems, optimization. It also has many links with applications in engineering, finance, quantum physics, and other fields. This book covers recent and diverse aspects of stochastic and infinite-dimensional analysis. The included papers are written from a variety of standpoints (white noise analysis, Malliavin calculus, quantum stochastic calculus) by the contributors, and provide a broad coverage of the subject. This volume will be useful to graduate students and research mathematicians wishing to get acquainted with recent developments in the field of stochastic analysis.
Book Synopsis Stochastic Calculus of Variations by : Yasushi Ishikawa
Download or read book Stochastic Calculus of Variations written by Yasushi Ishikawa and published by . This book was released on 2023-07-24 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Stochastic Differential Equations by : Peter H. Baxendale
Download or read book Stochastic Differential Equations written by Peter H. Baxendale and published by World Scientific. This book was released on 2007 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of 15 articles written by experts in stochastic analysis. The first paper in the volume, Stochastic Evolution Equations by N V Krylov and B L Rozovskii, was originally published in Russian in 1979. After more than a quarter-century, this paper remains a standard reference in the field of stochastic partial differential equations (SPDEs) and continues to attract the attention of mathematicians of all generations. Together with a short but thorough introduction to SPDEs, it presents a number of optimal, and essentially unimprovable, results about solvability for a large class of both linear and non-linear equations. The other papers in this volume were specially written for the occasion of Prof RozovskiiOCOs 60th birthday. They tackle a wide range of topics in the theory and applications of stochastic differential equations, both ordinary and with partial derivatives."
Book Synopsis Control Theory, Stochastic Analysis And Applications - Proceedings Of Symposium On System Sciences And Control Theory by : S P Chen
Download or read book Control Theory, Stochastic Analysis And Applications - Proceedings Of Symposium On System Sciences And Control Theory written by S P Chen and published by World Scientific. This book was released on 1992-03-27 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: The symposium discusses and explores the current and future development of some aspects of the theory of nonlinear control systems, adaptive control and filtering, robust control and H∞ optimization, stochastic systems and white noise analysis, etc.
Book Synopsis Backward Stochastic Differential Equations by : N El Karoui
Download or read book Backward Stochastic Differential Equations written by N El Karoui and published by CRC Press. This book was released on 1997-01-17 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the texts of seminars presented during the years 1995 and 1996 at the Université Paris VI and is the first attempt to present a survey on this subject. Starting from the classical conditions for existence and unicity of a solution in the most simple case-which requires more than basic stochartic calculus-several refinements on the hypotheses are introduced to obtain more general results.
Book Synopsis Handbook of Stochastic Analysis and Applications by : D. Kannan
Download or read book Handbook of Stochastic Analysis and Applications written by D. Kannan and published by CRC Press. This book was released on 2001-10-23 with total page 808 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to general theories of stochastic processes and modern martingale theory. The volume focuses on consistency, stability and contractivity under geometric invariance in numerical analysis, and discusses problems related to implementation, simulation, variable step size algorithms, and random number generation.
Book Synopsis Advances in Deterministic and Stochastic Analysis by :
Download or read book Advances in Deterministic and Stochastic Analysis written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Stochastic Differential Equations and Applications by : Avner Friedman
Download or read book Stochastic Differential Equations and Applications written by Avner Friedman and published by . This book was released on 1975 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt:
