Harnack Inequalities For Stochastic Partial Differential Equations
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Harnack Inequalities For Stochastic Partial Differential Equations
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Author : Feng-Yu Wang
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-08-13
Harnack Inequalities For Stochastic Partial Differential Equations written by Feng-Yu Wang 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 2013-08-13 with Mathematics categories.
In this book the author presents a self-contained account of Harnack inequalities and applications for the semigroup of solutions to stochastic partial and delayed differential equations. Since the semigroup refers to Fokker-Planck equations on infinite-dimensional spaces, the Harnack inequalities the author investigates are dimension-free. This is an essentially different point from the above mentioned classical Harnack inequalities. Moreover, the main tool in the study is a new coupling method (called coupling by change of measures) rather than the usual maximum principle in the current literature.
Stochastic Partial Differential Equations And Related Fields
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Author : Andreas Eberle
language : en
Publisher: Springer
Release Date : 2018-07-03
Stochastic Partial Differential Equations And Related Fields written by Andreas Eberle and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-03 with Mathematics categories.
This Festschrift contains five research surveys and thirty-four shorter contributions by participants of the conference ''Stochastic Partial Differential Equations and Related Fields'' hosted by the Faculty of Mathematics at Bielefeld University, October 10–14, 2016. The conference, attended by more than 140 participants, including PostDocs and PhD students, was held both to honor Michael Röckner's contributions to the field on the occasion of his 60th birthday and to bring together leading scientists and young researchers to present the current state of the art and promising future developments. Each article introduces a well-described field related to Stochastic Partial Differential Equations and Stochastic Analysis in general. In particular, the longer surveys focus on Dirichlet forms and Potential theory, the analysis of Kolmogorov operators, Fokker–Planck equations in Hilbert spaces, the theory of variational solutions to stochastic partial differential equations, singular stochastic partial differential equations and their applications in mathematical physics, as well as on the theory of regularity structures and paracontrolled distributions. The numerous research surveys make the volume especially useful for graduate students and researchers who wish to start work in the above-mentioned areas, or who want to be informed about the current state of the art.
Distribution Dependent Stochastic Differential Equations
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Author : Feng-yu Wang
language : en
Publisher: World Scientific
Release Date : 2024-09-26
Distribution Dependent Stochastic Differential Equations written by Feng-yu Wang and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-26 with Mathematics categories.
Corresponding to the link of Itô's stochastic differential equations (SDEs) and linear parabolic equations, distribution dependent SDEs (DDSDEs) characterize nonlinear Fokker-Planck equations. This type of SDEs is named after McKean-Vlasov due to the pioneering work of H P McKean (1966), where an expectation dependent SDE is proposed to characterize nonlinear PDEs for Maxwellian gas. Moreover, by using the propagation of chaos for Kac particle systems, weak solutions of DDSDEs are constructed as weak limits of mean field particle systems when the number of particles goes to infinity, so that DDSDEs are also called mean-field SDEs. To restrict a DDSDE in a domain, we consider the reflection boundary by following the line of A V Skorohod (1961).This book provides a self-contained account on singular SDEs and DDSDEs with or without reflection. It covers well-posedness and regularities for singular stochastic differential equations; well-posedness for singular reflected SDEs; well-posedness of singular DDSDEs; Harnack inequalities and derivative formulas for singular DDSDEs; long time behaviors for DDSDEs; DDSDEs with reflecting boundary; and killed DDSDEs.
Asymptotic Analysis For Functional Stochastic Differential Equations
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Author : Jianhai Bao
language : en
Publisher: Springer
Release Date : 2016-11-19
Asymptotic Analysis For Functional Stochastic Differential Equations written by Jianhai Bao and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-19 with Mathematics categories.
This brief treats dynamical systems that involve delays and random disturbances. The study is motivated by a wide variety of systems in real life in which random noise has to be taken into consideration and the effect of delays cannot be ignored. Concentrating on such systems that are described by functional stochastic differential equations, this work focuses on the study of large time behavior, in particular, ergodicity.This brief is written for probabilists, applied mathematicians, engineers, and scientists who need to use delay systems and functional stochastic differential equations in their work. Selected topics from the brief can also be used in a graduate level topics course in probability and stochastic processes.
Fokker Planck Kolmogorov Equations
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Author : Vladimir I. Bogachev
language : en
Publisher: American Mathematical Society
Release Date : 2022-02-10
Fokker Planck Kolmogorov Equations written by Vladimir I. Bogachev and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-10 with Mathematics categories.
This book gives an exposition of the principal concepts and results related to second order elliptic and parabolic equations for measures, the main examples of which are Fokker–Planck–Kolmogorov equations for stationary and transition probabilities of diffusion processes. Existence and uniqueness of solutions are studied along with existence and Sobolev regularity of their densities and upper and lower bounds for the latter. The target readership includes mathematicians and physicists whose research is related to diffusion processes as well as elliptic and parabolic equations.
Stochastic Partial Differential Equations And Applications
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Author : Giuseppe Da Prato
language : en
Publisher: CRC Press
Release Date : 2002-04-05
Stochastic Partial Differential Equations And Applications written by Giuseppe Da Prato and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-04-05 with Mathematics categories.
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.
Stochastic Equations In Infinite Dimensions
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Author : Giuseppe Da Prato
language : en
Publisher: Cambridge University Press
Release Date : 2014-04-17
Stochastic Equations In Infinite Dimensions written by Giuseppe Da Prato and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-04-17 with Mathematics categories.
Updates in this second edition include two brand new chapters and an even more comprehensive bibliography.
Non Divergence Equations Structured On Hormander Vector Fields Heat Kernels And Harnack Inequalities
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Author : Marco Bramanti
language : en
Publisher: American Mathematical Soc.
Release Date : 2010
Non Divergence Equations Structured On Hormander Vector Fields Heat Kernels And Harnack Inequalities written by Marco Bramanti and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
"March 2010, Volume 204, number 961 (end of volume)."
Stochastic Analysis
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Author : Michael Craig Cranston
language : en
Publisher: American Mathematical Soc.
Release Date : 1995
Stochastic Analysis written by Michael Craig Cranston and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Mathematics categories.
This book deals with current developments in stochastic analysis and its interfaces with partial differential equations, dynamical systems, mathematical physics, differential geometry, and infinite-dimensional analysis. The origins of stochastic analysis can be found in Norbert Wiener's construction of Brownian motion and Kiyosi Itô's subsequent development of stochastic integration and the closely related theory of stochastic (ordinary) differential equations. The papers in this volume indicate the great strides that have been made in recent years, exhibiting the tremendous power and diversity of stochastic analysis while giving a clear indication of the unsolved problems and possible future directions for development. The collection represents the proceedings of the AMS Summer Institute on Stochastic Analysis, held in July 1993 at Cornell University. Many of the papers are largely expository in character while containing new results.
Modern Problems Of Stochastic Analysis And Statistics
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Author : Vladimir Panov
language : en
Publisher: Springer
Release Date : 2017-11-21
Modern Problems Of Stochastic Analysis And Statistics written by Vladimir Panov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-21 with Mathematics categories.
This book brings together the latest findings in the area of stochastic analysis and statistics. The individual chapters cover a wide range of topics from limit theorems, Markov processes, nonparametric methods, acturial science, population dynamics, and many others. The volume is dedicated to Valentin Konakov, head of the International Laboratory of Stochastic Analysis and its Applications on the occasion of his 70th birthday. Contributions were prepared by the participants of the international conference of the international conference “Modern problems of stochastic analysis and statistics”, held at the Higher School of Economics in Moscow from May 29 - June 2, 2016. It offers a valuable reference resource for researchers and graduate students interested in modern stochastics.