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On conditional diffusion processes

Published online by Cambridge University Press:  14 November 2011

T. J. Lyons  and
W. A. Zheng
T. J. Lyons
Affiliation:
Department of Mathematics, University of Edinburgh, James Clerk Maxwell Building, The King's Buildings, Mayfield Road, Edinburgh EH9 3JZ, Scotland, U.K.
W. A. Zheng
Affiliation:
Department of Mathematics, University of Edinburgh, James Clerk Maxwell Building, The King's Buildings, Mayfield Road, Edinburgh EH9 3JZ, Scotland, U.K.
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Synopsis

If Xt is the diffusion process associated with a second-order uniformly elliptic operator L in divergence form, then without assuming smoothness in L we prove that for each x and y in ℝd,

where p is the fundamental solution to the heat equation associated with L. This allows one to control p when bounded drift terms are added to L; and also allows one to do Stratonovich integration with respect to the process conditioned to start at any point; previous work only dealt with quasi-every starting point.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 115 , Issue 3-4 , 1990 , pp. 243 - 255
Copyright
Copyright © Royal Society of Edinburgh 1990

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References

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