Stochastic Differential Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Stochastic Differential Equations write by Peter H. Baxendale. This book was released on 2007. Stochastic Differential Equations available in PDF, EPUB and Kindle. The first paper in the volume, Stochastic Evolution Equations by N V Krylov and B L Rozovskii, was originally published in Russian in 1979. After more than a quarter-century, this paper remains a standard reference in the field of stochastic partial differential equations (SPDEs) and continues to attract attention of mathematicians of all generations, because, together with a short but thorough introduction to SPDEs, it presents a number of optimal and essentially non-improvable results about solvability for a large class of both linear and non-linear equations.
Stochastic Evolution Systems
Stochastic Evolution Systems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Stochastic Evolution Systems write by Boris L. Rozovsky. This book was released on 2018-10-03. Stochastic Evolution Systems available in PDF, EPUB and Kindle. This monograph, now in a thoroughly revised second edition, develops the theory of stochastic calculus in Hilbert spaces and applies the results to the study of generalized solutions of stochastic parabolic equations. The emphasis lies on second-order stochastic parabolic equations and their connection to random dynamical systems. The authors further explore applications to the theory of optimal non-linear filtering, prediction, and smoothing of partially observed diffusion processes. The new edition now also includes a chapter on chaos expansion for linear stochastic evolution systems. This book will appeal to anyone working in disciplines that require tools from stochastic analysis and PDEs, including pure mathematics, financial mathematics, engineering and physics.
Strong and Weak Approximation of Semilinear Stochastic Evolution Equations
Strong and Weak Approximation of Semilinear Stochastic Evolution Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Strong and Weak Approximation of Semilinear Stochastic Evolution Equations write by Raphael Kruse. This book was released on 2013-11-18. Strong and Weak Approximation of Semilinear Stochastic Evolution Equations available in PDF, EPUB and Kindle. In this book we analyze the error caused by numerical schemes for the approximation of semilinear stochastic evolution equations (SEEq) in a Hilbert space-valued setting. The numerical schemes considered combine Galerkin finite element methods with Euler-type temporal approximations. Starting from a precise analysis of the spatio-temporal regularity of the mild solution to the SEEq, we derive and prove optimal error estimates of the strong error of convergence in the first part of the book. The second part deals with a new approach to the so-called weak error of convergence, which measures the distance between the law of the numerical solution and the law of the exact solution. This approach is based on Bismut’s integration by parts formula and the Malliavin calculus for infinite dimensional stochastic processes. These techniques are developed and explained in a separate chapter, before the weak convergence is proven for linear SEEq.
Stochastic Integrals
Stochastic Integrals - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Stochastic Integrals write by Henry P. McKean. This book was released on 2024-05-23. Stochastic Integrals available in PDF, EPUB and Kindle. This little book is a brilliant introduction to an important boundary field between the theory of probability and differential equations. —E. B. Dynkin, Mathematical Reviews This well-written book has been used for many years to learn about stochastic integrals. The book starts with the presentation of Brownian motion, then deals with stochastic integrals and differentials, including the famous Itô lemma. The rest of the book is devoted to various topics of stochastic integral equations, including those on smooth manifolds. Originally published in 1969, this classic book is ideal for supplementary reading or independent study. It is suitable for graduate students and researchers interested in probability, stochastic processes, and their applications.
Stochastic Evolution Equations
Stochastic Evolution Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Stochastic Evolution Equations write by Wilfried Grecksch. This book was released on 1995. Stochastic Evolution Equations available in PDF, EPUB and Kindle. The authors give a self-contained exposition of the theory of stochastic evolution equations. Elements of infinite dimensional analysis, martingale theory in Hilbert spaces, stochastic integrals, stochastic convolutions are applied. Existence and uniqueness theorems for stochastic evolution equations in Hilbert spaces in the sense of the semigroup theory, the theory of evolution operators, and monotonous operators in rigged Hilbert spaces are discussed. Relationships between the different concepts are demonstrated. The results are used to concrete stochastic partial differential equations like parabolic and hyperbolic Ito equations and random constitutive equations of elastic viscoplastic materials. Furthermore, stochastic evolution equations in rigged Hilbert spaces are approximated by time discretization methods.
