ISSN:
1432-2064
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Summary Let (ρ t ϕ)0≦t≦1 be the unnormalized filter arising in the filtering theory of correlated diffusions. In this article, ϱ. φ. is considered as a stochastic process taking values inC(ℝ n ,ℝ); a description of the support of its law in the Fréchet spaceC([0,1],C(ℝ n ,R)) is given. This result is the analogue for stochastic partial differential equations of the celebrated Stroock-Varadhan theorem for diffusion processes. The support of the law of the filter is shown to be the closure of the set of trajectories obtained from the Zakai equation by replacing the Stratonovitch differentialdy by anH 1-control (herey denotes the observation process).
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01288562
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