Download or read book Topics Related to Backward Stochastic Differential Equations Driven by L vy Processes written by 周清 and published by . This book was released on 2019 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Forward Backward Stochastic Differential Equations and their Applications written by Jin Ma and published by Springer. This book was released on 2007-04-24 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a survey/monograph on the recently developed theory of forward-backward stochastic differential equations (FBSDEs). Basic techniques such as the method of optimal control, the 'Four Step Scheme', and the method of continuation are presented in full. Related topics such as backward stochastic PDEs and many applications of FBSDEs are also discussed in detail. The volume is suitable for readers with basic knowledge of stochastic differential equations, and some exposure to the stochastic control theory and PDEs. It can be used for researchers and/or senior graduate students in the areas of probability, control theory, mathematical finance, and other related fields.
Download or read book Backward Stochastic Differential Equations G expectations and Related Topics written by Qian Lin and published by . This book was released on 2011 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: We first study Nash equilibrium payoffs for nonzero sum stochastic differential games with nonlinear cost functionals. We obtain an existence theorem and a characterization theorem for Nash equilibria. The obtained results extend former ones by Buckdahn, Cardaliaguet ami Rainer (2004). The generalization concerns the following aspects: Firstly, our cost functionals are defined by controlled backward stochastic differential equations, and the admissible control processes depend on events occurring before the beginning of the stochastic differential game. Thus, our cost functionals are not necessarily deterministic. Secondly, since our cost functionals are nonlinear and can be coupled, we cannot apply the methods used in Buckdahn, Cardaliaguet and Rainer. We make use of the notion of stochastic backward and the theory of backward stochastic differential equations. I've also been studying selected problems of G-expectations, among them the notion of local time for which I've obtained the Tanaka formula for the G-Brownian motion as well as the joint continuity of the local time of the G-Brownian motion. Moreover, I've derived a representation of G-martingales as stochastic integrals with respect to G-Brownian motion, which generalizes the martingale characterization theorem for G-Brownian motion established by Xu. Finally, I also have studied one-dimensional backward doubly stochastic differential equations with non-Lipschitz coefficient for which I get an existence result.
Download or read book Applied Stochastic Differential Equations written by Simo Särkkä and published by Cambridge University Press. This book was released on 2019-05-02 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: With this hands-on introduction readers will learn what SDEs are all about and how they should use them in practice.
Download or read book Backward Stochastic Differential Equations Driven by Gaussian Volterra Processes written by Habiba Knani and published by . This book was released on 2020 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis treats of backward stochastic differential equations (BSDE) driven by a class of Gaussian Volterra processes that includes multifractional Brownian motion and multifractional Ornstein-Uhlenbeck processes. In the first part we study multidimensional BSDE with generators that are linear functions of the solution. By means of an Itoˆ formula for Volterra processes, a linear second order partial differential equation (PDE) with terminal condition is associated to the BSDE. Under an integrability condition on a functional of the second moment of the Volterra process in a neighbourhood of the terminal time, we solve the associated PDE explicitely and deduce the solution of the linear BSDE. We discuss an application in the context of self-financing trading stategies. The second part of the thesis treats of non-linear BSDE driven by the same class of Gaussian Volterra processes. The main results are the existence and uniqueness of the solution in a space of regular functionals of the Volterra process, and a comparison theorem for the solutions of BSDE. We give two proofs for the existence and uniqueness of the solution, one is based on the associated PDE and a second one without making reference to this PDE, but with probabilistic and functional theoretic methods. Especially this second proof is technically quite complex, and, due to the absence of mar- tingale properties in the context of Volterra processes, requires to work with different norms on the underlying Hilbert space that is defined by the kernel of the Volterra process. For the construction of the solution we need the notion of quasi-conditional expectation, a Clark-Ocone type formula and another Itoˆ formula for Volterra processes. Contrary to the more classical cases of BSDE driven by Brownian or fractional Brownian motion, an assumption on the behaviour of the kernel of the driv- ing Volterra process is in general necessary for the wellposedness of the BSDE. For multifractional Brownian motion this assumption is closely related to the behaviour of the Hurst function.
Download or read book L vy Processes and Stochastic Calculus written by David Applebaum and published by Cambridge University Press. This book was released on 2009-04-30 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lévy processes form a wide and rich class of random process, and have many applications ranging from physics to finance. Stochastic calculus is the mathematics of systems interacting with random noise. Here, the author ties these two subjects together, beginning with an introduction to the general theory of Lévy processes, then leading on to develop the stochastic calculus for Lévy processes in a direct and accessible way. This fully revised edition now features a number of new topics. These include: regular variation and subexponential distributions; necessary and sufficient conditions for Lévy processes to have finite moments; characterisation of Lévy processes with finite variation; Kunita's estimates for moments of Lévy type stochastic integrals; new proofs of Ito representation and martingale representation theorems for general Lévy processes; multiple Wiener-Lévy integrals and chaos decomposition; an introduction to Malliavin calculus; an introduction to stability theory for Lévy-driven SDEs.
Download or read book Stochastic Differential Equations and Processes written by Mounir Zili and published by Springer Science & Business Media. This book was released on 2011-09-24 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: Selected papers submitted by participants of the international Conference “Stochastic Analysis and Applied Probability 2010” ( www.saap2010.org ) make up the basis of this volume. The SAAP 2010 was held in Tunisia, from 7-9 October, 2010, and was organized by the “Applied Mathematics & Mathematical Physics” research unit of the preparatory institute to the military academies of Sousse (Tunisia), chaired by Mounir Zili. The papers cover theoretical, numerical and applied aspects of stochastic processes and stochastic differential equations. The study of such topic is motivated in part by the need to model, understand, forecast and control the behavior of many natural phenomena that evolve in time in a random way. Such phenomena appear in the fields of finance, telecommunications, economics, biology, geology, demography, physics, chemistry, signal processing and modern control theory, to mention just a few. As this book emphasizes the importance of numerical and theoretical studies of the stochastic differential equations and stochastic processes, it will be useful for a wide spectrum of researchers in applied probability, stochastic numerical and theoretical analysis and statistics, as well as for graduate students. To make it more complete and accessible for graduate students, practitioners and researchers, the editors Mounir Zili and Daria Filatova have included a survey dedicated to the basic concepts of numerical analysis of the stochastic differential equations, written by Henri Schurz.
Download or read book Topics on Backward Stochastic Differential Equations written by Arnaud Lionnet and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Backward Stochastic Differential Equations written by Jianfeng Zhang and published by Springer. This book was released on 2017-08-22 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a systematic and accessible approach to stochastic differential equations, backward stochastic differential equations, and their connection with partial differential equations, as well as the recent development of the fully nonlinear theory, including nonlinear expectation, second order backward stochastic differential equations, and path dependent partial differential equations. Their main applications and numerical algorithms, as well as many exercises, are included. The book focuses on ideas and clarity, with most results having been solved from scratch and most theories being motivated from applications. It can be considered a starting point for junior researchers in the field, and can serve as a textbook for a two-semester graduate course in probability theory and stochastic analysis. It is also accessible for graduate students majoring in financial engineering.
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 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 2005-04-20 with total page 458 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.
Download or read book Stochastic Differential Equations and Related Topics written by Liangjian Hu and published by . This book was released on 2007 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Topics in Ergodic Control and Backward Stochastic Differential Equations written by Victor Fedyashov and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Stochastic Differential Equations written by Tony G. Deangelo and published by . This book was released on 2018 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: "In this collection, the authors begin by introducing a methodology for examining continuous-time Ornstein-Uhlenbech family processes defined by stochastic differential equations (SDEs). Additionally, a study is presented introducing the mathematics of mixed effect parameters in univariate and bivariate SDEs and describing how such a model can be used to aid our understanding of growth processes using real world datasets. Results and experience from applying the concepts and techniques in an extensive individual tree and stand growth modeling program in Lithuania are described as examples. Next, the authors present a review paper on J-calculus, as well as a contributed paper which displays some new results on the topic and deepens some special properties in relation with non-differentiability of functions. Following this, this book develops the general framework to be used in our papers [2, 9, 8]. The starting point for the discussion will be the standard risk-sensitive structures, and how constructions of this kind can be given a rigorous treatment. The risk-sensitive optimal control is also investigated by using the extending part of this of problem of backward stochastic equation. In the closing article, the authors note that the square of an O-U process is the Cox-Ingersoll-Ross process used as a model for volatility in finance. The filtered form of the original hazard rate based on this new observation is also studied. If the difference between the original hazard rate and the filtered one is not significant, then the person is not affected by the new frailty"--
Download or read book Introduction To Differential Equations An Stochastic Modeling Methods And Analysis Volume 2 written by Anilchandra G Ladde and published by World Scientific Publishing Company. This book was released on 2013-01-11 with total page 634 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volume 1: Deterministic Modeling, Methods and Analysis For more than half a century, stochastic calculus and stochastic differential equations have played a major role in analyzing the dynamic phenomena in the biological and physical sciences, as well as engineering. The advancement of knowledge in stochastic differential equations is spreading rapidly across the graduate and postgraduate programs in universities around the globe. This will be the first available book that can be used in any undergraduate/graduate stochastic modeling/applied mathematics courses and that can be used by an interdisciplinary researcher with a minimal academic background. An Introduction to Differential Equations: Volume 2 is a stochastic version of Volume 1 (“An Introduction to Differential Equations: Deterministic Modeling, Methods and Analysis”). Both books have a similar design, but naturally, differ by calculi. Again, both volumes use an innovative style in the presentation of the topics, methods and concepts with adequate preparation in deterministic Calculus. Errata Errata (32 KB)
Download or read book Variational and Ergodic Methods for Stochastic Differential Equations Driven by L vy Processes written by Jan Martin Gairing and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
