Abstract
Of concern is a class of second-order differential operators on the unit interval. The C0-semigroup generated by them is approximated by iterates of positive linear operators that are introduced here as a modification of Bernstein operators. Finally, the corresponding stochastic differential equations are also investigated, leading, in particular to the evaluation of the asymptotic behaviour of the semigroup.
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Keywords
- Approximation Theory
- Bernstein Polynomial
- Positive Linear Operator
- Bernstein Operator
- Convex Continuous Function
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Altomare, F., Rasa, I. (2005). On Some Classes of Diffusion Equations and Related Approximation Problems. In: Mache, D.H., Szabados, J., de Bruin, M.G. (eds) Trends and Applications in Constructive Approximation. ISNM International Series of Numerical Mathematics, vol 151. Birkhäuser Basel. https://doi.org/10.1007/3-7643-7356-3_2
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DOI: https://doi.org/10.1007/3-7643-7356-3_2
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