Author: Guillermo Ferreyra
Publisher:
ISBN:
Category : Semimartingales (Mathematics)
Languages : en
Pages : 17
Book Description
Solutions of stochastic differential equations having differentials of bounded variation processes on the right hand side can be defined by means of Lebesgue Stieltjes integrals or by continuous extension of Stieltjes integrals. Both solutions are compared here and formulas that extend the Wong-Zakai theorem are obtained.
A Wong-Zakai Type Theorem for Certain Discontinuous Semimartingales
Author: Guillermo Ferreyra
Publisher:
ISBN:
Category : Semimartingales (Mathematics)
Languages : en
Pages : 17
Book Description
Solutions of stochastic differential equations having differentials of bounded variation processes on the right hand side can be defined by means of Lebesgue Stieltjes integrals or by continuous extension of Stieltjes integrals. Both solutions are compared here and formulas that extend the Wong-Zakai theorem are obtained.
Publisher:
ISBN:
Category : Semimartingales (Mathematics)
Languages : en
Pages : 17
Book Description
Solutions of stochastic differential equations having differentials of bounded variation processes on the right hand side can be defined by means of Lebesgue Stieltjes integrals or by continuous extension of Stieltjes integrals. Both solutions are compared here and formulas that extend the Wong-Zakai theorem are obtained.
Scientific and Technical Aerospace Reports
Author:
Publisher:
ISBN:
Category : Aeronautics
Languages : en
Pages : 956
Book Description
Publisher:
ISBN:
Category : Aeronautics
Languages : en
Pages : 956
Book Description
Technical Reports Awareness Circular : TRAC.
Author:
Publisher:
ISBN:
Category : Science
Languages : en
Pages : 534
Book Description
Publisher:
ISBN:
Category : Science
Languages : en
Pages : 534
Book Description
Statistical Theory and Method Abstracts
Author:
Publisher:
ISBN:
Category : Statistics
Languages : en
Pages : 1070
Book Description
Publisher:
ISBN:
Category : Statistics
Languages : en
Pages : 1070
Book Description
Numerical Methods for Stochastic Partial Differential Equations with White Noise
Author: Zhongqiang Zhang
Publisher: Springer
ISBN: 3319575112
Category : Mathematics
Languages : en
Pages : 391
Book Description
This book covers numerical methods for stochastic partial differential equations with white noise using the framework of Wong-Zakai approximation. The book begins with some motivational and background material in the introductory chapters and is divided into three parts. Part I covers numerical stochastic ordinary differential equations. Here the authors start with numerical methods for SDEs with delay using the Wong-Zakai approximation and finite difference in time. Part II covers temporal white noise. Here the authors consider SPDEs as PDEs driven by white noise, where discretization of white noise (Brownian motion) leads to PDEs with smooth noise, which can then be treated by numerical methods for PDEs. In this part, recursive algorithms based on Wiener chaos expansion and stochastic collocation methods are presented for linear stochastic advection-diffusion-reaction equations. In addition, stochastic Euler equations are exploited as an application of stochastic collocation methods, where a numerical comparison with other integration methods in random space is made. Part III covers spatial white noise. Here the authors discuss numerical methods for nonlinear elliptic equations as well as other equations with additive noise. Numerical methods for SPDEs with multiplicative noise are also discussed using the Wiener chaos expansion method. In addition, some SPDEs driven by non-Gaussian white noise are discussed and some model reduction methods (based on Wick-Malliavin calculus) are presented for generalized polynomial chaos expansion methods. Powerful techniques are provided for solving stochastic partial differential equations. This book can be considered as self-contained. Necessary background knowledge is presented in the appendices. Basic knowledge of probability theory and stochastic calculus is presented in Appendix A. In Appendix B some semi-analytical methods for SPDEs are presented. In Appendix C an introduction to Gauss quadrature is provided. In Appendix D, all the conclusions which are needed for proofs are presented, and in Appendix E a method to compute the convergence rate empirically is included. In addition, the authors provide a thorough review of the topics, both theoretical and computational exercises in the book with practical discussion of the effectiveness of the methods. Supporting Matlab files are made available to help illustrate some of the concepts further. Bibliographic notes are included at the end of each chapter. This book serves as a reference for graduate students and researchers in the mathematical sciences who would like to understand state-of-the-art numerical methods for stochastic partial differential equations with white noise.
Publisher: Springer
ISBN: 3319575112
Category : Mathematics
Languages : en
Pages : 391
Book Description
This book covers numerical methods for stochastic partial differential equations with white noise using the framework of Wong-Zakai approximation. The book begins with some motivational and background material in the introductory chapters and is divided into three parts. Part I covers numerical stochastic ordinary differential equations. Here the authors start with numerical methods for SDEs with delay using the Wong-Zakai approximation and finite difference in time. Part II covers temporal white noise. Here the authors consider SPDEs as PDEs driven by white noise, where discretization of white noise (Brownian motion) leads to PDEs with smooth noise, which can then be treated by numerical methods for PDEs. In this part, recursive algorithms based on Wiener chaos expansion and stochastic collocation methods are presented for linear stochastic advection-diffusion-reaction equations. In addition, stochastic Euler equations are exploited as an application of stochastic collocation methods, where a numerical comparison with other integration methods in random space is made. Part III covers spatial white noise. Here the authors discuss numerical methods for nonlinear elliptic equations as well as other equations with additive noise. Numerical methods for SPDEs with multiplicative noise are also discussed using the Wiener chaos expansion method. In addition, some SPDEs driven by non-Gaussian white noise are discussed and some model reduction methods (based on Wick-Malliavin calculus) are presented for generalized polynomial chaos expansion methods. Powerful techniques are provided for solving stochastic partial differential equations. This book can be considered as self-contained. Necessary background knowledge is presented in the appendices. Basic knowledge of probability theory and stochastic calculus is presented in Appendix A. In Appendix B some semi-analytical methods for SPDEs are presented. In Appendix C an introduction to Gauss quadrature is provided. In Appendix D, all the conclusions which are needed for proofs are presented, and in Appendix E a method to compute the convergence rate empirically is included. In addition, the authors provide a thorough review of the topics, both theoretical and computational exercises in the book with practical discussion of the effectiveness of the methods. Supporting Matlab files are made available to help illustrate some of the concepts further. Bibliographic notes are included at the end of each chapter. This book serves as a reference for graduate students and researchers in the mathematical sciences who would like to understand state-of-the-art numerical methods for stochastic partial differential equations with white noise.
Mathematical Reviews
Author:
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 868
Book Description
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 868
Book Description
Rozprawy Matematyczne
Author:
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 388
Book Description
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 388
Book Description
Government Reports Annual Index
Author:
Publisher:
ISBN:
Category : Research
Languages : en
Pages : 1010
Book Description
Sections 1-2. Keyword Index.--Section 3. Personal author index.--Section 4. Corporate author index.-- Section 5. Contract/grant number index, NTIS order/report number index 1-E.--Section 6. NTIS order/report number index F-Z.
Publisher:
ISBN:
Category : Research
Languages : en
Pages : 1010
Book Description
Sections 1-2. Keyword Index.--Section 3. Personal author index.--Section 4. Corporate author index.-- Section 5. Contract/grant number index, NTIS order/report number index 1-E.--Section 6. NTIS order/report number index F-Z.
Proceedings of the 26th IEEE Conference on Decision and Control
Author:
Publisher:
ISBN:
Category : Adaptive control system
Languages : en
Pages : 930
Book Description
Publisher:
ISBN:
Category : Adaptive control system
Languages : en
Pages : 930
Book Description
Government Reports Annual Index: Keyword A-L
Author:
Publisher:
ISBN:
Category : Government reports announcements & index
Languages : en
Pages : 1600
Book Description
Publisher:
ISBN:
Category : Government reports announcements & index
Languages : en
Pages : 1600
Book Description