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Decreasing sequences of \(\sigma\)-fields and a measure change for Brownian motion. II. (English) Zbl 0870.60079
This paper is the sequel to and a sharpening of the paper reviewed above. Using similar techniques, the authors construct for a given real Brownian motion \((\Omega,{\mathfrak F},\mathbb{P},\{B(t)\}_{t\geq 0}, \{{\mathfrak F}_t\}_{t>0})\) a probability measure \(\mathbb{Q}\) such that (a) \((1-\varepsilon)\mathbb{P}\leq\mathbb{Q}\leq(1+ \varepsilon)\mathbb{P}\) (and not merely \(\mathbb{P}\ll\mathbb{Q}\ll\mathbb{P})\) and (b) \(\{{\mathfrak F}_t\}_{t\geq 0}\) cannot be generated by any Brownian motion on \((\Omega,{\mathfrak F},\mathbb{Q})\).

MSC:
60J65 Brownian motion
28C20 Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.)
60G07 General theory of stochastic processes
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
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