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One-dimensional diffusions and approximation. (English) Zbl 1116.47037

The author considers a second order differential operator \(A\) acting in the space of continuous as well as in the space of square integrable functions. The Voronovskaya type approximations of the associated infinitesimal generator and its solution semigroup are studied. The stochastic equation associated with \(A\) is considered and some explicit specific solutions are presented.

MSC:

47D06 One-parameter semigroups and linear evolution equations
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
41A36 Approximation by positive operators
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