Commutative Conformable Fractional Korovkin Approximation for Stochastic Processes

Here we research the expectation commutative stochastic positive linear operators acting on L1-continuous stochastic processes which are conformable fractional differentiable. Under some mild, general and natural assumptions on the stochastic processes we produce related conformable fractional stochastic Shisha-Mond type inequalities pointwise and uniform

Trigonometric Commutative Caputo Fractional Korovkin Approximation for Stochastic Processes

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 αth right and left fractional derivatives of the engaged stochastic process, (Formula Presented)

Trigonometric Commutative Conformable Fractional Korovkin Approximation for Stochastic Processes

Here we research from the trigonometric point of view expectation commutative stochastic positive linear operators acting on L1-continuous stochastic processes which are Conformable fractional differentiable. Under some mild, general and natural assumptions on the stochastic processes we produce related trigonometric Conformable fractional stochastic Shisha-Mond type inequalities pointwise and uniform

Commutative Caputo Fractional Korovkin Approximation for Stochastic Processes

Here we consider and study 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 Caputo fractional stochastic Shisha-Mond type inequalities pointwise and uniform. All convergences are produced with rates and are given by the fractional stochastic inequalities involving the first modulus of continuity of the expectation of the αth right and left fractional derivatives of the engaged stochastic process, (Formula Presented). The amazing fact here is that the basic real Korovkin test functions assumptions impose the conclusions of our Caputo fractional stochastic Korovkin theory. We include also a detailed application to stochastic Bernstein operators. See also[11]

A note on LeCam’s bound for the distance between the Poisson binomial and the Poisson distribution

Poisson binomial distribution, Poisson approximation, total variation distance,

Optimized regression model for time series

SIGLEDEGerman

Trigonometric Conformable Fractional Approximation of Stochastic Processes

Here we consider very general stochastic positive linear operators induced by general positive linear operators that are acting on continuous functions in the trigonometric sense. 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 trigonometric conformable fractional stochastic Shisha-Mond type inequalities of Lq-type (Formula Presented) and corresponding trigonometric conformable fractional stochastic Korovkin type theorems

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 \u3e0, (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[9]

Trigonometric Caputo Fractional Approximation of Stochastic Processes

Here we encounter and study very general stochastic positive linear operators induced by general positive linear operators that are acting on continuous functions in the trigonometric sense. These are acting on the space of real fractionally differentiable stochastic processes. Under some very mild, general and natural assumptions on the stochastic processes we produce related trigonometric fractional stochastic Shisha-Mond type inequalities of Lq-type (Formula Presented) and corresponding trigonometric fractional stochastic Korovkin type theorems. These are regarding the trigonometric stochastic q-mean 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 trigonometric fractional stochastic inequalities involving the stochastic modulus of continuity of the αth fractional derivatives of the engaged stochastic process, (Formula Presented). The impressive fact is that only two basic real Korovkin test functions assumptions, one of them trigonometric, are enough for the conclusions of our trigonometric fractional stochastic Korovkin theory. We give applications to stochastic Bernstein operators in the trigonometric sense. See also [11]