Conformable Fractional Quantitative Approximation of Stochastic Processes
Here we consider and study very general stochastic positive linear operators induced by general positive linear operators that are acting on continuous functions. These are acting on the space of real conformable fractionally differentiable stochastic processes. Under some very mild, general and natural assumptions on the stochastic processes we produce related conformable fractional stochastic Shisha-Mond type inequalities of Lq-type (Formula Presented) and corresponding conformable fractional stochastic Korovkin type theorems. These are regarding the stochastic q -mean conformable fractional convergence of a sequence of stochastic positive linear operators to the stochastic unit operator for various cases. All convergences are produced with rates and are given via the conformable fractional stochastic inequalities involving the stochastic modulus of continuity of the αth conformable fractional derivatives of the engaged stochastic process, α >0, (Formula Presented). The impressive fact is that the basic real Korovkin test functions assumptions are enough for the conclusions of our conformable fractional stochastic Korovkin theory. We give conformable fractional applications to stochastic Bernstein operators. See also.
Studies in Systems, Decision and Control
Anastassiou, G. (2021). Conformable Fractional Quantitative Approximation of Stochastic Processes. Studies in Systems, Decision and Control, 305, 355-393. https://doi.org/10.1007/978-3-030-56962-4_16