One-Dimensional Diffusions and Approximation |
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Authors: | Ioan Rasa |
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Affiliation: | (1) Department of Mathematics, Technical University of Cluj-Napoca, C. Daicoviciu 15, 400020 Cluj-Napoca, Romania |
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Abstract: | Consider the Voronovskaja operator A of a sequence of positive linear operators and let u(t, x) be the solution of the Cauchy problem for A. In the spirit of Altomare’s theory this solution can be studied by using the semigroup (T(t))t ≥ 0 generated by A and represented in terms of the operators Ln.One associates to A a stochastic equation; its solution can be also used in order to represent u(t, x).The relations between all these objects are described in the case of the operator A associated with some Meyer-König and Zeller type operators. |
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Keywords: | 47D06 60H10 41A36 |
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