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A decomposition of additive functionals of finite energy

Published online by Cambridge University Press:  22 January 2016

Masatoshi Fukushima
Masatoshi Fukushima*
Affiliation:
College of General Education Osaka University
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The celebrated Ito formula for the n-dimensional Brownian motion Xt and for u ∈ C2(Rn) runs as follows:

(0.1)

In § 6 of this paper we extend this to the case where u is any element of the Sobolev space H1R(n) and accordingly Δu is a tempered distribution which is not even a signed measure in general. As a consequence the second term of the right hand side of (0.1) may not be of bounded variation in t.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 74 , July 1979 , pp. 137 - 168
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1979

References

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