| EPSRC Reference: |
GR/S75628/01 |
| Title: |
Approximation schemes & anticipation in stochastic integration |
| Principal Investigator: |
Lyons, Professor T |
| Other Investigators: |
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| Department: |
Mathematical Institute |
| Organisation: |
University of Oxford |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
20 October 2003 |
Ends: |
19 October 2005 |
Value (£): |
3,783
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| EPSRC Research Topic Classifications: |
| Mathematical Analysis |
Numerical Analysis |
| Statistics & Appl. Probability |
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| EPSRC Industrial Sector Classifications: |
| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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Building on earlier work, Ito introduced a general method for producing maps which take one stochastic process of semimartigale type into another. Although It's methodology has wide applicability, it has flaws. Namely, the procedure for passing from the implicit to the explicit description of Ito's map requires a delicate device involving stochastic integration and a non-anticipating integrand. As the level of Noise subsides one would expect convergence to classical systems - the proof is delicate and part of the famous work of Stroock and Varadhan.Important, and distinctive approaches now exist extending this approach in fundamental ways. The theory of stochastic integration starting with Stratonovich can now be extended (using the theory of rough paths) to sources of randomness like (for example) fractional Brownian motion that were outside the original approach. The third theory of stochastic integration is Skorohod's attempt to get away from non-anticipating integrands. The most elegant way to think about Skorohod's integral is in terms of the differentiable structure of Wiener space.Our goal is to integrate these ideas from classical deterministic and stochastic analysis somewhat better than they are at the moment. For example we would like to understand Skorohod's theory in terms of the micro-analytic ideas about the multiplication of distributions whose wave front sets mesh well. Of particular importance for an increasing number of applications would be the development of a theory which allow for a robust, implementable approximation scheme for Skorohod integration.
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Key Findings |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Potential use in non-academic contexts |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Impacts |
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| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
| Summary |
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| Date Materialised |
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Sectors submitted by the Researcher |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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| Project URL: |
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| Further Information: |
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| Organisation Website: |
http://www.ox.ac.uk |