This article is cited in 7 papers

On the coincidence of $\sigma$-algebras in the filtration problem for diffusion processes

N. V. Krylov

Moscow

Abstract: Multidimensional diffusion process (1) with two components is considered. The main theorem states that two $\sigma$-algebras (one generated by the observable process $y_t$ and another generated by its innovation $\overline w_t$ and initial condition $y_0$) coincide.

Received: 12.10.1977

 English version: Theory of Probability and its Applications, 1980, 24:4, 772–781

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