Download or read book Invariant Measures for a Stochastic Porous Medium Equation written by Giuseppe Da Prato and published by . This book was released on 2003 with total page 17 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Stochastic Porous Media Equations written by Viorel Barbu and published by Springer. This book was released on 2016-09-30 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focusing on stochastic porous media equations, this book places an emphasis on existence theorems, asymptotic behavior and ergodic properties of the associated transition semigroup. Stochastic perturbations of the porous media equation have reviously been considered by physicists, but rigorous mathematical existence results have only recently been found. The porous media equation models a number of different physical phenomena, including the flow of an ideal gas and the diffusion of a compressible fluid through porous media, and also thermal propagation in plasma and plasma radiation. Another important application is to a model of the standard self-organized criticality process, called the "sand-pile model" or the "Bak-Tang-Wiesenfeld model". The book will be of interest to PhD students and researchers in mathematics, physics and biology.

Download or read book Kolmogorov Equations for Stochastic PDEs written by Giuseppe Da Prato and published by Birkhäuser. This book was released on 2012-12-06 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: Kolmogorov Equations for Stochastic PDEs gives an introduction to stochastic partial differential equations, such as reaction-diffusion, Burgers and 2D Navier-Stokes equations, perturbed by noise. It studies several properties of corresponding transition semigroups, such as Feller and strong Feller properties, irreducibility, existence and uniqueness of invariant measures. In addition, the transition semigroups are interpreted as generalized solutions of Kologorov equations.

Download or read book Stochastic Equations in Infinite Dimensions written by Giuseppe Da Prato and published by Cambridge University Press. This book was released on 2014-04-17 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt: Updates in this second edition include two brand new chapters and an even more comprehensive bibliography.

Download or read book Xivth International Congress On Mathematical Physics written by Jean-claude Zambrini and published by World Scientific. This book was released on 2006-03-07 with total page 718 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 2003 the XIV International Congress on Mathematical Physics (ICMP) was held in Lisbon with more than 500 participants. Twelve plenary talks were given in various fields of Mathematical Physics: E Carlen «On the relation between the Master equation and the Boltzmann Equation in Kinetic Theory»; A Chenciner «Symmetries and “simple” solutions of the classical n-body problem»; M J Esteban «Relativistic models in atomic and molecular physics»; K Fredenhagen «Locally covariant quantum field theory»; K Gawedzki «Simple models of turbulent transport»; I Krichever «Algebraic versus Liouville integrability of the soliton systems»; R V Moody «Long-range order and diffraction in mathematical quasicrystals»; S Smirnov «Critical percolation and conformal invariance»; J P Solovej «The energy of charged matter»; V Schomerus «Strings through the microscope»; C Villani «Entropy production and convergence to equilibrium for the Boltzmann equation»; D Voiculescu «Aspects of free probability».The book collects as well carefully selected invited Session Talks in: Dynamical Systems, Integrable Systems and Random Matrix Theory, Condensed Matter Physics, Equilibrium Statistical Mechanics, Quantum Field Theory, Operator Algebras and Quantum Information, String and M Theory, Fluid Dynamics and Nonlinear PDE, General Relativity, Nonequilibrium Statistical Mechanics, Quantum Mechanics and Spectral Theory, Path Integrals and Stochastic Analysis.

Download or read book Invariant Measures for Stochastic Partial Differential Equations and Splitting up Method for Stochastic Flows written by Juan Yang and published by . This book was released on 2012 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Stochastic Methods for Flow in Porous Media written by Dongxiao Zhang and published by Elsevier. This book was released on 2001-10-11 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic Methods for Flow in Porous Media: Coping with Uncertainties explores fluid flow in complex geologic environments. The parameterization of uncertainty into flow models is important for managing water resources, preserving subsurface water quality, storing energy and wastes, and improving the safety and economics of extracting subsurface mineral and energy resources. This volume systematically introduces a number of stochastic methods used by researchers in the community in a tutorial way and presents methodologies for spatially and temporally stationary as well as nonstationary flows. The author compiles a number of well-known results and useful formulae and includes exercises at the end of each chapter. Balanced viewpoint of several stochastic methods, including Greens' function, perturbative expansion, spectral, Feynman diagram, adjoint state, Monte Carlo simulation, and renormalization group methods Tutorial style of presentation will facilitate use by readers without a prior in-depth knowledge of Stochastic processes Practical examples throughout the text Exercises at the end of each chapter reinforce specific concepts and techniques For the reader who is interested in hands-on experience, a number of computer codes are included and discussed

Download or read book Invariant Measures for Stochastic Partial Differential Equations and Splitting up Method for Stochastic Flows written by Juan Yang and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis consists of two parts. We start with some background theory that will be used throughout the thesis. Then, in the first part, we investigate the existence and uniqueness of the solution of the stochastic partial differential equation with two reflecting walls. Then we establish the existence and uniqueness of invariant measure of this equation under some reasonable conditions. In the second part, we study the splitting-up method for approximating the solu- tions of stochastic Stokes equations using resolvent method.

Download or read book Kolmogorov s Heritage in Mathematics written by Eric Charpentier and published by Springer Science & Business Media. This book was released on 2007-09-13 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, several world experts present (one part of) the mathematical heritage of Kolmogorov. Each chapter treats one of his research themes or a subject invented as a consequence of his discoveries. The authors present his contributions, his methods, the perspectives he opened to us, and the way in which this research has evolved up to now. Coverage also includes examples of recent applications and a presentation of the modern prospects.

Download or read book Fokker Planck Kolmogorov Equations written by Vladimir I. Bogachev and published by American Mathematical Society. This book was released on 2022-02-10 with total page 495 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Stochastic PDEs and Dynamics written by Boling Guo and published by Walter de Gruyter GmbH & Co KG. This book was released on 2016-11-21 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explains mathematical theories of a collection of stochastic partial differential equations and their dynamical behaviors. Based on probability and stochastic process, the authors discuss stochastic integrals, Ito formula and Ornstein-Uhlenbeck processes, and introduce theoretical framework for random attractors. With rigorous mathematical deduction, the book is an essential reference to mathematicians and physicists in nonlinear science. Contents: Preliminaries The stochastic integral and Itô formula OU processes and SDEs Random attractors Applications Bibliography Index

Download or read book Stochastic Partial Differential Equations and Applications VII written by Giuseppe Da Prato and published by CRC Press. This book was released on 2005-10-12 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic Partial Differential Equations and Applications gives an overview of current state-of-the-art stochastic PDEs in several fields, such as filtering theory, stochastic quantization, quantum probability, and mathematical finance. Featuring contributions from leading expert participants at an international conference on the subject, this boo

Download or read book Stochastic Analysis and Related Topics in Kyoto written by Kiyosi Itō and published by American Mathematical Society(RI). This book was released on 2004 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of research and survey papers written by invited lecturers at the RIMS international symposium on stochastic analysis and related topics in celebration of Professor Kiyosi Itt's eighty-eighth birthday. It also covers topics such as quadratic Wiener functionals, representation of martingales, and Itt's construction procedure.

Download or read book Stochastic PDE s and Kolmogorov Equations in Infinite Dimensions written by N.V. Krylov and published by Springer. This book was released on 2006-11-15 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: Kolmogorov equations are second order parabolic equations with a finite or an infinite number of variables. They are deeply connected with stochastic differential equations in finite or infinite dimensional spaces. They arise in many fields as Mathematical Physics, Chemistry and Mathematical Finance. These equations can be studied both by probabilistic and by analytic methods, using such tools as Gaussian measures, Dirichlet Forms, and stochastic calculus. The following courses have been delivered: N.V. Krylov presented Kolmogorov equations coming from finite-dimensional equations, giving existence, uniqueness and regularity results. M. Röckner has presented an approach to Kolmogorov equations in infinite dimensions, based on an LP-analysis of the corresponding diffusion operators with respect to suitably chosen measures. J. Zabczyk started from classical results of L. Gross, on the heat equation in infinite dimension, and discussed some recent results.

Download or read book Large Deviations and Invariant Measures for Stochastic Partial Differential Equations in Infinite Dimensions written by Tiange Xu and published by . This book was released on 2009 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Theoretical and Numerical Analysis of Invariant Measures of Viscous Stochastic Scalar Conservation Laws written by Sofiane Martel and published by . This book was released on 2019 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This devoted to the theoretical and numerical analysis of a certain class of stochastic partial differential equations (SPDEs), namely scalar conservation laws with viscosity and with a stochastic forcing which is an additive white noise in time. A particular case of interest is the stochastic Burgers equation, which is motivated by turbulence theory. We focus on the long time behaviour of the solutions of these equations through a study of the invariant measures. The theoretical part of the thesis constitutes the second chapter. In this chapter, we prove the existence and uniqueness of a solution in a strong sense. To this end, estimates on Sobolev norms up to the second order are established. In the second part of Chapter~2, we show that the solution of the SPDE admits a unique invariant measure. In the third chapter, we aim to approximate numerically this invariant measure. For this purpose, we introduce a numerical scheme whose spatial discretisation is of the finite volume type and whose temporal discretisation is a split-step backward Euler method. It is shown that this kind of scheme preserves some fundamental properties of the SPDE such as energy dissipation and L^1-contraction. Those properties ensure the existence and uniqueness of an invariant measure for the numerical scheme. Thanks to a few regularity estimates, we show that this discrete invariant measure converges, as the space and time steps tend to zero, towards the unique invariant measure for the SPDE in the sense of the second order Wasserstein distance. Finally, numerical experiments are performed on the Burgers equation in order to illustrate this convergence as well as some small-scale properties related to turbulence.

Download or read book Stochastic Partial Differential Equations and Related Fields written by Andreas Eberle and published by Springer. This book was released on 2018-07-03 with total page 574 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.