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A property of distributions of diffusion processes. (English. Russian original) Zbl 0826.60065
Math. Notes 54, No. 3, 946-950 (1993); translation from Mat. Zametki 54, No. 3, 106-113 (1993).
Let $$\mu_X$$ be a distribution of the diffusion process defined by the equation $$dX_t = a(X_t) dW_t$$, where $$a$$ is a bounded analytic function. It is proved that there exists a set $$B$$ in the space of trajectories $$C ([0,1])$$ of complete $$\mu_X$$-measures such that for any $$y,h \in C ([0,1])$$ the set on the line $$\{t : y + th \in B\}$$ is at most countable. This means that $$\mu_X$$ is located on the exceptional set in the Aronszajn sense.

MSC:
 60J60 Diffusion processes 60A10 Probabilistic measure theory
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References:
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