Diffusion Processes And Partial Differential Equations
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Diffusion Processes And Partial Differential Equations
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Author : Kazuaki Taira
language : en
Publisher:
Release Date : 1988
Diffusion Processes And Partial Differential Equations written by Kazuaki Taira and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Mathematics categories.
This book provides a careful and accessible exposition of functional analytic methods in stochastic analysis. It focuses on the relationship between Markov processes and elliptic boundary value problems and explores several recent developments in the theory of partial differential equations which have made further progress in the study of Markov processes possible. This book will have great appeal to both advanced students and researchers as an introduction to three interrelated subjects in analysis (Markov processes, semigroups, and elliptic boundary value problems), providing powerful methods for future research.
Partial Differential Equations And Diffusion Processes
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Author : Russell Godding
language : en
Publisher:
Release Date : 2018-11-22
Partial Differential Equations And Diffusion Processes written by Russell Godding and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-22 with categories.
In probability theory and statistics, a diffusion process is a solution to a stochastic differential equation. It is a continuous-time Markov process with almost surely continuous sample paths. Brownian motion, reflected Brownian motion and Ornstein-Uhlenbeck processes are examples of diffusion processes. A sample path of a diffusion process models the trajectory of a particle embedded in a flowing fluid and subjected to random displacements due to collisions with other particles, which is called Brownian motion. The position of the particle is then random; its probability density function as a function of space and time is governed by an advection-diffusion equation.
Stochastic Analysis And Diffusion Processes
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Author : Gopinath Kallianpur
language : en
Publisher: OUP Oxford
Release Date : 2014-01-09
Stochastic Analysis And Diffusion Processes written by Gopinath Kallianpur and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-09 with Mathematics categories.
Stochastic Analysis and Diffusion Processes presents a simple, mathematical introduction to Stochastic Calculus and its applications. The book builds the basic theory and offers a careful account of important research directions in Stochastic Analysis. The breadth and power of Stochastic Analysis, and probabilistic behavior of diffusion processes are told without compromising on the mathematical details. Starting with the construction of stochastic processes, the book introduces Brownian motion and martingales. The book proceeds to construct stochastic integrals, establish the Itô formula, and discuss its applications. Next, attention is focused on stochastic differential equations (SDEs) which arise in modeling physical phenomena, perturbed by random forces. Diffusion processes are solutions of SDEs and form the main theme of this book. The Stroock-Varadhan martingale problem, the connection between diffusion processes and partial differential equations, Gaussian solutions of SDEs, and Markov processes with jumps are presented in successive chapters. The book culminates with a careful treatment of important research topics such as invariant measures, ergodic behavior, and large deviation principle for diffusions. Examples are given throughout the book to illustrate concepts and results. In addition, exercises are given at the end of each chapter that will help the reader to understand the concepts better. The book is written for graduate students, young researchers and applied scientists who are interested in stochastic processes and their applications. The reader is assumed to be familiar with probability theory at graduate level. The book can be used as a text for a graduate course on Stochastic Analysis.
Diffusion Processes And Related Problems In Analysis Volume Ii
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Author : V. Wihstutz
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Diffusion Processes And Related Problems In Analysis Volume Ii written by V. Wihstutz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
During the weekend of March 16-18, 1990 the University of North Carolina at Charlotte hosted a conference on the subject of stochastic flows, as part of a Special Activity Month in the Department of Mathematics. This conference was supported jointly by a National Science Foundation grant and by the University of North Carolina at Charlotte. Originally conceived as a regional conference for researchers in the Southeastern United States, the conference eventually drew participation from both coasts of the U. S. and from abroad. This broad-based par ticipation reflects a growing interest in the viewpoint of stochastic flows, particularly in probability theory and more generally in mathematics as a whole. While the theory of deterministic flows can be considered classical, the stochastic counterpart has only been developed in the past decade, through the efforts of Harris, Kunita, Elworthy, Baxendale and others. Much of this work was done in close connection with the theory of diffusion processes, where dynamical systems implicitly enter probability theory by means of stochastic differential equations. In this regard, the Charlotte conference served as a natural outgrowth of the Conference on Diffusion Processes, held at Northwestern University, Evanston Illinois in October 1989, the proceedings of which has now been published as Volume I of the current series. Due to this natural flow of ideas, and with the assistance and support of the Editorial Board, it was decided to organize the present two-volume effort.
Applied Diffusion Processes From Engineering To Finance
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Author : Jacques Janssen
language : en
Publisher: John Wiley & Sons
Release Date : 2013-04-08
Applied Diffusion Processes From Engineering To Finance written by Jacques Janssen and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-08 with Mathematics categories.
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.
Entropy Methods For Diffusive Partial Differential Equations
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Author : Ansgar Jüngel
language : en
Publisher: Springer
Release Date : 2016-06-17
Entropy Methods For Diffusive Partial Differential Equations written by Ansgar Jüngel and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-17 with Mathematics categories.
This book presents a range of entropy methods for diffusive PDEs devised by many researchers in the course of the past few decades, which allow us to understand the qualitative behavior of solutions to diffusive equations (and Markov diffusion processes). Applications include the large-time asymptotics of solutions, the derivation of convex Sobolev inequalities, the existence and uniqueness of weak solutions, and the analysis of discrete and geometric structures of the PDEs. The purpose of the book is to provide readers an introduction to selected entropy methods that can be found in the research literature. In order to highlight the core concepts, the results are not stated in the widest generality and most of the arguments are only formal (in the sense that the functional setting is not specified or sufficient regularity is supposed). The text is also suitable for advanced master and PhD students and could serve as a textbook for special courses and seminars.
Diffusion Processes Jump Processes And Stochastic Differential Equations
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Author : Wojbor A. Woyczyński
language : en
Publisher: CRC Press
Release Date : 2022-03-09
Diffusion Processes Jump Processes And Stochastic Differential Equations written by Wojbor A. Woyczyński and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-09 with Mathematics categories.
Diffusion Processes, Jump Processes, and Stochastic Differential Equations provides a compact exposition of the results explaining interrelations between diffusion stochastic processes, stochastic differential equations and the fractional infinitesimal operators. The draft of this book has been extensively classroom tested by the author at Case Western Reserve University in a course that enrolled seniors and graduate students majoring in mathematics, statistics, engineering, physics, chemistry, economics and mathematical finance. The last topic proved to be particularly popular among students looking for careers on Wall Street and in research organizations devoted to financial problems. Features Quickly and concisely builds from basic probability theory to advanced topics Suitable as a primary text for an advanced course in diffusion processes and stochastic differential equations Useful as supplementary reading across a range of topics.
Regional Analysis Of Time Fractional Diffusion Processes
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Author : Fudong Ge
language : en
Publisher: Springer
Release Date : 2018-01-08
Regional Analysis Of Time Fractional Diffusion Processes written by Fudong Ge and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-08 with Technology & Engineering categories.
This monograph provides an accessible introduction to the regional analysis of fractional diffusion processes. It begins with background coverage of fractional calculus, functional analysis, distributed parameter systems and relevant basic control theory. New research problems are then defined in terms of their actuation and sensing policies within the regional analysis framework. The results presented provide insight into the control-theoretic analysis of fractional-order systems for use in real-life applications such as hard-disk drives, sleep stage identification and classification, and unmanned aerial vehicle control. The results can also be extended to complex fractional-order distributed-parameter systems and various open questions with potential for further investigation are discussed. For instance, the problem of fractional order distributed-parameter systems with mobile actuators/sensors, optimal parameter identification, optimal locations/trajectory of actuators/sensors and regional actuation/sensing configurations are of great interest. The book’s use of illustrations and consistent examples throughout helps readers to understand the significance of the proposed fractional models and methodologies and to enhance their comprehension. The applications treated in the book run the gamut from environmental science to national security. Academics and graduate students working with cyber-physical and distributed systems or interested in the applications of fractional calculus will find this book to be an instructive source of state-of-the-art results and inspiration for further research.
Diffusions And Elliptic Operators
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Author : Richard F. Bass
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-05-11
Diffusions And Elliptic Operators written by Richard F. Bass and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-05-11 with Mathematics categories.
A discussion of the interplay of diffusion processes and partial differential equations with an emphasis on probabilistic methods. It begins with stochastic differential equations, the probabilistic machinery needed to study PDE, and moves on to probabilistic representations of solutions for PDE, regularity of solutions and one dimensional diffusions. The author discusses in depth two main types of second order linear differential operators: non-divergence operators and divergence operators, including topics such as the Harnack inequality of Krylov-Safonov for non-divergence operators and heat kernel estimates for divergence form operators, as well as Martingale problems and the Malliavin calculus. While serving as a textbook for a graduate course on diffusion theory with applications to PDE, this will also be a valuable reference to researchers in probability who are interested in PDE, as well as for analysts interested in probabilistic methods.
Inverse Problems In Diffusion Processes
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Author : Heinz W. Engl
language : en
Publisher: SIAM
Release Date : 1995-01-01
Inverse Problems In Diffusion Processes written by Heinz W. Engl and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-01-01 with Mathematics categories.
This collection of expository papers encompasses both the theoretical and physical application side of inverse problems in diffusion processes.