A property of distributions of diffusion processes
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.
scientific article; zbMATH DE number 687509