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Stochastic Analysis 2010

  • Book
  • © 2011

Overview

Editors:
  1. Dan Crisan

    1. Department of Mathematics, Imperial College London, London, United Kingdom

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  • aims to provide mathematical tools to describe and model high dimensional random systems.

  • provides a sample of the current research in the different branches of Stochastic Analysis

  • 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

  • Includes supplementary material: sn.pub/extras

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Table of contents (14 chapters)

  1. Front Matter

    Pages i-viii
    Download chapter PDF

  2. Introduction

    • Dan Crisan
    Pages 1-6

  3. Integration by Parts Formula with Respect to Jump Times for StochasticDifferential Equations

    • Vlad Bally, Emmanuelle Clément
    Pages 7-29

  4. A Laplace Principle for a Stochastic Wave Equation in Spatial Dimension Three

    • Víctor Ortiz-López, Marta Sanz-Solé
    Pages 31-49

  5. Intertwinned Diffusions by Examples

    • Xue-Mei Li
    Pages 51-71

  6. Efficient and Practical Implementations of Cubature on Wiener Space

    • Lajos Gergely Gyurkó, Terry J. Lyons
    Pages 73-111

  7. Equivalence of Stochastic Equations and Martingale Problems

    • Thomas G. Kurtz
    Pages 113-130

  8. Accelerated Numerical Schemes for PDEs and SPDEs

    • István Gyöngy, Nicolai Krylov
    Pages 131-168

  9. Coarse-Grained Modeling of Multiscale Diffusions: The p-Variation Estimates

    • Anastasia Papavasiliou
    Pages 169-190

  10. Numerical Solution of the Dirichlet Problem for Linear Parabolic SPDEs Based on Averaging over Characteristics

    • Vasile N. Stanciulescu, Michael V. Tretyakov
    Pages 191-212

  11. Individual Path Uniqueness of Solutions of Stochastic Differential Equations

    • Alexander M. Davie
    Pages 213-225

  12. Stochastic Integrals and SDE Driven by Nonlinear Lévy Noise

    • Vassili N. Kolokoltsov
    Pages 227-242

  13. Discrete Algorithms for Multivariate Financial Calculus

    • Radu Tunaru
    Pages 243-266

  14. Credit Risk, Market Sentiment and Randomly-Timed Default

    • Dorje C. Brody, Lane P. Hughston, Andrea Macrina
    Pages 267-280

  15. Continuity of Mutual Entropy in the Limiting Signal-To-Noise Ratio Regimes

    • Mark Kelbert, Yuri Suhov
    Pages 281-299
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Keywords

About this book

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.

Editors and Affiliations

  • Department of Mathematics, Imperial College London, London, United Kingdom

    Dan Crisan

About the editor

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.

Bibliographic Information

  • Book Title: Stochastic Analysis 2010

  • Editors: Dan Crisan

  • DOI: https://doi.org/10.1007/978-3-642-15358-7

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2011

  • Hardcover ISBN: 978-3-642-15357-0Published: 30 November 2010

  • Softcover ISBN: 978-3-642-42284-3Published: 02 October 2014

  • eBook ISBN: 978-3-642-15358-7Published: 26 November 2010

  • Edition Number: 1

  • Number of Pages: VIII, 299

  • Topics: Probability Theory and Stochastic Processes

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