EPSRC Reference: 
GR/S75628/01 
Title: 
Approximation schemes & anticipation in stochastic integration 
Principal Investigator: 
Lyons, Professor T 
Other Investigators: 

Researcher CoInvestigators: 

Project Partners: 

Department: 
Mathematical Institute 
Organisation: 
University of Oxford 
Scheme: 
Standard Research (PreFEC) 
Starts: 
20 October 2003 
Ends: 
19 October 2005 
Value (£): 
3,783

EPSRC Research Topic Classifications: 
Mathematical Analysis 
Numerical Analysis 
Statistics & Appl. Probability 


EPSRC Industrial Sector Classifications: 
No relevance to Underpinning Sectors 


Related Grants: 

Panel History: 

Summary on Grant Application Form 
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 nonanticipating 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 nonanticipating 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 microanalytic 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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Organisation Website: 
http://www.ox.ac.uk 