Stochastic Integrals and Evolution Equations with Gaussian Random Fields

Stochastic Integrals and Evolution Equations with Gaussian Random Fields The paper studies stochastic integration with respect to Gaussian processes and fields. It is more convenient to work with a field than a process: by definition, a field is a collection of stochastic integrals for a class of deterministic integrands. The problem is then to extend the definition to random integrands. An orthogonal decomposition of the chaos space of the random field, combined with the Wick product, leads to the Itô-Skorokhod integral, and provides an efficient tool to study the integral, both analytically and numerically. For a Gaussian process, a natural definition of the integral follows from a canonical correspondence between random processes and a special class of random fields. Also considered are the corresponding linear stochastic evolution equations. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

Stochastic Integrals and Evolution Equations with Gaussian Random Fields

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Publisher
Springer-Verlag
Copyright
Copyright © 2009 by Springer Science+Business Media, LLC
Subject
Mathematics; Numerical and Computational Methods ; Mathematical Methods in Physics; Mathematical and Computational Physics; Systems Theory, Control; Calculus of Variations and Optimal Control; Optimization
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s00245-008-9051-z
Publisher site
See Article on Publisher Site

Abstract

The paper studies stochastic integration with respect to Gaussian processes and fields. It is more convenient to work with a field than a process: by definition, a field is a collection of stochastic integrals for a class of deterministic integrands. The problem is then to extend the definition to random integrands. An orthogonal decomposition of the chaos space of the random field, combined with the Wick product, leads to the Itô-Skorokhod integral, and provides an efficient tool to study the integral, both analytically and numerically. For a Gaussian process, a natural definition of the integral follows from a canonical correspondence between random processes and a special class of random fields. Also considered are the corresponding linear stochastic evolution equations.

Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Apr 1, 2009

References

  • Stochastic analysis of the fractional Brownian motion
    Decreusefond, L.; Üstünel, A.S.

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