Synopses & Reviews
Stochastic Analysis aims to provide mathematical tools to describe and model high dimensional random systems. Such tools arise in the study of Stochastic Differential Equations and Stochastic Partial Differential Equations, Infinite Dimensional Stochastic Geometry, Random Media and Interacting Particle Systems, Super-processes, Stochastic Filtering, Mathematical Finance, etc. Stochastic Analysis has emerged as a core area of late 20th century Mathematics and is currently undergoing a rapid scientific development. The special volume "Stochastic Analysis 2010" provides a sample of the current research in the different branches of the subject. It includes the collected works of the participants at the Stochastic Analysis section of the 7th ISAAC Congress organized at Imperial College London in July 2009.
Synopsis
Stochastic Analysis provides mathematical tools to both describe and model high dimensional random systems. The text presents a sample of the current research in the different branches of the subject, including collected works of the participants at the the 7th ISAAC Congress at Imperial College London, July 2009.
Synopsis
Stochastic Analysis provides mathematical tools to both describe and model high dimensional random systems. The text presents a sample of the current research in the different branches of the subject, including collected works of the participants at the the 7th ISAAC Congress at Imperial College London, July 2009.
About the Author
Dr. Dan Crisan is a Reader in Mathematics at Imperial College London, whose expertise area lies in Stochastic Analysis with applications in Engineering and Finance. His main area of research is stochastic filtering theory, a topic which deals with the estimation of partially observed signals. Some of the many applications of stochastic filtering are signal processing, satellite tracking, global positioning systems, spell checkers, weather forecasting, EEG/ECG analysis and computer vision. In 2009 Springer published his book Fundamentals of Stochastic Filtering. Dr. Crisan is member of the editorial board of the Journal of Mathematics and Computation. He is also actively involved in teaching. Among numerous other courses, he has taught stochastic filtering, numerical Stochastics, and measure-valued processes at Imperial College; applied probability, and stochastic calculus and applications at Cambridge University.
Table of Contents
D.Crisan: Introduction to the Volume.- V. Bally and E. Clément: Integration by Parts Formula with Respect to Jump Times for Stochastic Differential Equations.- V. Ortiz-López and M. Sanz-Solé: A Laplace Principle for a Stochastic Wave Equation in Spatial Dimension Three.- X.-M. Li: Intertwinned Diffusions Operators by Examples.- L. G. Gyurkó and T. Lyons: Effcient and practical implementations of Cubature on Wiener space.- T. Kurtz: Equivalence of Stochastic Equations and Martingale Problems.- I. Gyöngy and N.V. Krylov: Accelerated Numerical Schemes for PDEs and SPDEs.- A. Papavasilio: Coarse-Grained Modeling of Multiscale Diffusions: The p-variation Estimates.- V.N. Stanciulescu and M.V. Tretyakov: Numerical Solution of the Dirichlet Problem for Linear Parabolic SPDEs Based on Averaging over Characteristics.- S. Davie: Individual Path Uniqueness of Solutions of Stochastic differential equations.- V. Kolokoltsov: Stochastic Integrals and SDE Driven by Nonlinear Levy Noise.- R. Tunaru: Discrete Algorithms for Multivariate Financial Calculus.- D. Brody, L. Hughston and A. Macrina: Credit Risk, Market Sentiment, and Randomly-Timed Default.- M. Kelbert and Y. Suhov: Continuity of mutual entropy in the limiting signal-to-noise ratio regimes.