An approach to Ito linear equations in Hilbert spaces by approximation of white noise with coloured noise
- 1 January 1984
- journal article
- research article
- Published by Taylor & Francis in Stochastic Analysis and Applications
- Vol. 2 (2) , 131-186
- https://doi.org/10.1080/07362998408809031
Abstract
We consider the stochastic problem , in a Hilbert space H, where f,X are prescribed data, Wt is a real Brownian motion, and A(t), B generate an analytic semi-group and a strongly continuous group respectively. The domains D(A (t)) may vary with t and we only require D(A(t))CD(B) for each t. A unique generalized solution is constructed as the pathwise uniform limit of solutions of suitable approximating deterministic problems, which are obtained by approaching the white noise dWt with a sequence of regular coloured noisesKeywords
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