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Basic Stochastic Processes
Stochastic processes are tools used widely by statisticians and researchers working in the mathematics of finance. This book for self-study provides a detailed treatment of conditional expectation and probability, a topic that in principle belongs to probability theory, but is essential as a tool for stochastic processes. The book centers on exercises as the main means of explanation.
Stochastic Partial Differential Equations and Applications - VII
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
Probabilistic Methods in Fluids
This volume contains recent research papers presented at the international workshop on ?Probabilistic Methods in Fluids? held in Swansea. The central problems considered were turbulence and the Navier-Stokes equations but, as is now well known, these classical problems are deeply intertwined with modern studies of stochastic partial differential equations, jump processes and random dynamical systems. The volume provides a snapshot of current studies in a field where the applications range from the design of aircraft through the mathematics of finance to the study of fluids in porous media.
Stochastic Analysis And Applications: Proceedings Of The Fifth Gregynog Symposium
This volume contains papers which were presented at a meeting entitled “Stochastic Analysis and Applications“ held at Gregynog Hall, Powys, from the 9th — 14th July 1995. The meeting consisted of a mixture of plenary/review talks and special interest sessions covering most of the current areas of activity in stochastic analysis. The meeting was jointly organized by the Department of Mathematics, University of Wales Swansea and the Mathematics Institute, University of Warwick in connection with the Stochastic Analysis year of activity. The papers contained herein are accessible to workers in the field of stochastic analysis and give a good coverage of topics of current interest in the research community.
Recent Development in Stochastic Dynamics and Stochastic Analysis
1. Hyperbolic equations with random boundary conditions / Zdzisław Brzeźniak and Szymon Peszat -- 2. Decoherent information of quantum operations / Xuelian Cao, Nan Li and Shunlong Luo -- 3. Stabilization of evolution equations by noise / Tomás Caraballo and Peter E. Kloeden -- 4. Stochastic quantification of missing mechanisms in dynamical systems / Baohua Chen and Jinqiao Duan -- 5. Banach space-valued functionals of white noise / Yin Chen and Caishi Wang -- 6. Hurst index estimation for self-similar processes with long-memory / Alexandra Chronopoulou and Frederi G. Viens -- 7. Modeling colored noise by fractional Brownian motion / Jinqiao Duan, Chujin Li and Xiangjun Wang -- 8. A suffi...
Stochastic Partial Differential Equations and Related Fields
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 Equ...
New Trends in Stochastic Analysis and Related Topics
The volume is dedicated to Professor David Elworthy to celebrate his fundamental contribution and exceptional influence on stochastic analysis and related fields. Stochastic analysis has been profoundly developed as a vital fundamental research area in mathematics in recent decades. It has been discovered to have intrinsic connections with many other areas of mathematics such as partial differential equations, functional analysis, topology, differential geometry, dynamical systems, etc. Mathematicians developed many mathematical tools in stochastic analysis to understand and model random phenomena in physics, biology, finance, fluid, environment science, etc. This volume contains 12 comprehe...
The Hodge-Laplacian
The core of this monograph is the development of tools to derive well-posedness results in very general geometric settings for elliptic differential operators. A new generation of Calderón-Zygmund theory is developed for variable coefficient singular integral operators, which turns out to be particularly versatile in dealing with boundary value problems for the Hodge-Laplacian on uniformly rectifiable subdomains of Riemannian manifolds via boundary layer methods. In addition to absolute and relative boundary conditions for differential forms, this monograph treats the Hodge-Laplacian equipped with classical Dirichlet, Neumann, Transmission, Poincaré, and Robin boundary conditions in regula...
Stochastic Analysis: A Series of Lectures
This book presents in thirteen refereed survey articles an overview of modern activity in stochastic analysis, written by leading international experts. The topics addressed include stochastic fluid dynamics and regularization by noise of deterministic dynamical systems; stochastic partial differential equations driven by Gaussian or Lévy noise, including the relationship between parabolic equations and particle systems, and wave equations in a geometric framework; Malliavin calculus and applications to stochastic numerics; stochastic integration in Banach spaces; porous media-type equations; stochastic deformations of classical mechanics and Feynman integrals and stochastic differential eq...
The Asymptotic Behaviour of Semigroups of Linear Operators
This book presents a systematic account of the theory of asymptotic behaviour of semigroups of linear operators acting in a Banach space. The focus is on the relationship between asymptotic behaviour of the semigroup and spectral properties of its infinitesimal generator. The most recent developments in the field are included, such as the Arendt-Batty-Lyubich-Vu theorem, the spectral mapp- ing theorem of Latushkin and Montgomery-Smith, Weis's theorem on stability of positive semigroup in Lp-spaces, the stability theorem for semigroups whose resolvent is bounded in a half-plane, and a systematic theory of individual stability. Addressed to researchers and graduate students with interest in the fields of operator semigroups and evolution equations, this book is self-contained and provides complete proofs.
