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Trigonometric Commutative Caputo Fractional Korovkin Theory for Stochastic Processes |
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PP: 293-305 |
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doi:10.18576/pfda/070408
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Author(s) |
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George A. Anastassiou,
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Abstract |
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| Here we consider and study from the trigonometric point of view expectation commutative stochastic positive linear operators acting on L1-continuous stochastic processes which are Caputo fractional differentiable. Under some mild, general and natural assumptions on the stochastic processes we produce related trigonometric Caputo fractional stochastic Shisha-Mond type inequalities pointwise and uniform. All convergences are produced with rates and are given by the trigonometric fractional stochastic inequalities involving the first modulus of continuity of the expectation of the α-th right and left fractional derivatives of the engaged stochastic process, α > 0, α ∈/ N. The amazing fact here is that the basic non-stochastic real Korovkin test functions assumptions impose the conclusions of our trigonometric Caputo fractional stochastic Korovkin theory. We include also a detailed trigonometric application to stochastic Bernstein operators.
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