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Functionals of diffusion processes as stochastic integrals

Published online by Cambridge University Press:  24 October 2008

M. H. A. Davis
Affiliation:
Department of Computing and Control, Imperial College, 180 Queen's Gate, London SW7 2BZ

Extract

Let be a standard d-dimensional Brownian motion and L a smooth functional on the space C = Cd[0, 1] of continuous functions from [0,1] to Rd, such that Denote Then

is a square integrable martingale which can be represented as a stochastic integral; consequently the random variable has the representation

For Fréchet differentiable functions L, Clark(1) gave the following formula for the integrand e:

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1980

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References

REFERENCES

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