On differentiability preserving properties of semigroups associated with one-dimensional singular diffusions. (English) Zbl 0562.60084

The author considers a one-dimensional diffusion on a finite interval. He shows that if the coefficient in the second derivative of the generator is not differentiable at boundary points then the semigroup of transition operators may not preserve the three-times differentiability of the initial data. Still, for sufficiently many initial data the one and two- times differentiability preserving properties hold true.
Reviewer: Y.Kifer


60J60 Diffusion processes
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60J50 Boundary theory for Markov processes
47D07 Markov semigroups and applications to diffusion processes
60J35 Transition functions, generators and resolvents
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