A decomposition of additive functionals of finite energy
- 1 July 1979
- journal article
- research article
- Published by Cambridge University Press (CUP) in Nagoya Mathematical Journal
- Vol. 74, 137-168
- https://doi.org/10.1017/s0027763000018493
Abstract
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.Keywords
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