Multidimensional Diffusion Processes

Download or read book Multidimensional Diffusion Processes written by Daniel W. Stroock and published by Springer. This book was released on 2007-02-03 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "This book is an excellent presentation of the application of martingale theory to the theory of Markov processes, especially multidimensional diffusions. [...] This monograph can be recommended to graduate students and research workers but also to all interested in Markov processes from a more theoretical point of view." Mathematische Operationsforschung und Statistik

Download or read book Inference for Diffusion Processes written by Christiane Fuchs and published by Springer Science & Business Media. This book was released on 2013-01-18 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: Diffusion processes are a promising instrument for realistically modelling the time-continuous evolution of phenomena not only in the natural sciences but also in finance and economics. Their mathematical theory, however, is challenging, and hence diffusion modelling is often carried out incorrectly, and the according statistical inference is considered almost exclusively by theoreticians. This book explains both topics in an illustrative way which also addresses practitioners. It provides a complete overview of the current state of research and presents important, novel insights. The theory is demonstrated using real data applications.

Download or read book Functionals of Multidimensional Diffusions with Applications to Finance written by Jan Baldeaux and published by Springer Science & Business Media. This book was released on 2013-08-13 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: This research monograph provides an introduction to tractable multidimensional diffusion models, where transition densities, Laplace transforms, Fourier transforms, fundamental solutions or functionals can be obtained in explicit form. The book also provides an introduction to the use of Lie symmetry group methods for diffusions, which allows to compute a wide range of functionals. Besides the well-known methodology on affine diffusions it presents a novel approach to affine processes with applications in finance. Numerical methods, including Monte Carlo and quadrature methods, are discussed together with supporting material on stochastic processes. Applications in finance, for instance, on credit risk and credit valuation adjustment are included in the book. The functionals of multidimensional diffusions analyzed in this book are significant for many areas of application beyond finance. The book is aimed at a wide readership, and develops an intuitive and rigorous understanding of the mathematics underlying the derivation of explicit formulas for functionals of multidimensional diffusions.​

Download or read book Diffusion Processes and Stochastic Calculus written by Fabrice Baudoin and published by Erich Schmidt Verlag GmbH & Co. KG. This book was released on 2014 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main purpose of the book is to present, at a graduate level and in a self-contained way, the most important aspects of the theory of continuous stochastic processes in continuous time and to introduce some of its ramifications such as the theory of semigroups, the Malliavin calculus, and the Lyons' rough paths. This book is intended for students, or even researchers, who wish to learn the basics in a concise but complete and rigorous manner. Several exercises are distributed throughout the text to test the understanding of the reader and each chapter ends with bibliographic comments aimed at those interested in exploring the materials further. Stochastic calculus was developed in the 1950s and the range of its applications is huge and still growing today. Besides being a fundamental component of modern probability theory, domains of applications include but are not limited to: mathematical finance, biology, physics, and engineering sciences. The first part of the text is devoted to the general theory of stochastic processes. The author focuses on the existence and regularity results for processes and on the theory of martingales. This allows him to introduce the Brownian motion quickly and study its most fundamental properties. The second part deals with the study of Markov processes, in particular, diffusions. The author's goal is to stress the connections between these processes and the theory of evolution semigroups. The third part deals with stochastic integrals, stochastic differential equations and Malliavin calculus. In the fourth and final part, the author presents an introduction to the very new theory of rough paths by Terry Lyons.

Download or read book Applied Diffusion Processes from Engineering to Finance written by Jacques Janssen and published by John Wiley & Sons. This book was released on 2013-04-08 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to promote interaction between engineering, finance and insurance, as these three domains have many models and methods of solution in common for solving real-life problems. The authors point out the strict inter-relations that exist among the diffusion models used in engineering, finance and insurance. In each of the three fields, the basic diffusion models are presented and their strong similarities are discussed. Analytical, numerical and Monte Carlo simulation methods are explained with a view to applying them to obtain the solutions to the different problems presented in the book. Advanced topics such as nonlinear problems, Lévy processes and semi-Markov models in interactions with the diffusion models are discussed, as well as possible future interactions among engineering, finance and insurance. Contents 1. Diffusion Phenomena and Models. 2. Probabilistic Models of Diffusion Processes. 3. Solving Partial Differential Equations of Second Order. 4. Problems in Finance. 5. Basic PDE in Finance. 6. Exotic and American Options Pricing Theory. 7. Hitting Times for Diffusion Processes and Stochastic Models in Insurance. 8. Numerical Methods. 9. Advanced Topics in Engineering: Nonlinear Models. 10. Lévy Processes. 11. Advanced Topics in Insurance: Copula Models and VaR Techniques. 12. Advanced Topics in Finance: Semi-Markov Models. 13. Monte Carlo Semi-Markov Simulation Methods.

Download or read book Relative Optimization of Continuous-Time and Continuous-State Stochastic Systems written by Xi-Ren Cao and published by Springer Nature. This book was released on 2020-05-13 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph applies the relative optimization approach to time nonhomogeneous continuous-time and continuous-state dynamic systems. The approach is intuitively clear and does not require deep knowledge of the mathematics of partial differential equations. The topics covered have the following distinguishing features: long-run average with no under-selectivity, non-smooth value functions with no viscosity solutions, diffusion processes with degenerate points, multi-class optimization with state classification, and optimization with no dynamic programming. The book begins with an introduction to relative optimization, including a comparison with the traditional approach of dynamic programming. The text then studies the Markov process, focusing on infinite-horizon optimization problems, and moves on to discuss optimal control of diffusion processes with semi-smooth value functions and degenerate points, and optimization of multi-dimensional diffusion processes. The book concludes with a brief overview of performance derivative-based optimization. Among the more important novel considerations presented are: the extension of the Hamilton–Jacobi–Bellman optimality condition from smooth to semi-smooth value functions by derivation of explicit optimality conditions at semi-smooth points and application of this result to degenerate and reflected processes; proof of semi-smoothness of the value function at degenerate points; attention to the under-selectivity issue for the long-run average and bias optimality; discussion of state classification for time nonhomogeneous continuous processes and multi-class optimization; and development of the multi-dimensional Tanaka formula for semi-smooth functions and application of this formula to stochastic control of multi-dimensional systems with degenerate points. The book will be of interest to researchers and students in the field of stochastic control and performance optimization alike.

Download or read book Stochastic Processes and Applications written by Grigorios A. Pavliotis and published by Springer. This book was released on 2014-11-19 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents various results and techniques from the theory of stochastic processes that are useful in the study of stochastic problems in the natural sciences. The main focus is analytical methods, although numerical methods and statistical inference methodologies for studying diffusion processes are also presented. The goal is the development of techniques that are applicable to a wide variety of stochastic models that appear in physics, chemistry and other natural sciences. Applications such as stochastic resonance, Brownian motion in periodic potentials and Brownian motors are studied and the connection between diffusion processes and time-dependent statistical mechanics is elucidated. The book contains a large number of illustrations, examples, and exercises. It will be useful for graduate-level courses on stochastic processes for students in applied mathematics, physics and engineering. Many of the topics covered in this book (reversible diffusions, convergence to equilibrium for diffusion processes, inference methods for stochastic differential equations, derivation of the generalized Langevin equation, exit time problems) cannot be easily found in textbook form and will be useful to both researchers and students interested in the applications of stochastic processes.