In this paper, we consider a general form of the increments for a two-parameter Wiener process. Both the Csorgo-Revesz's increments and a class of the lag increments are the special cases of this general form of i...In this paper, we consider a general form of the increments for a two-parameter Wiener process. Both the Csorgo-Revesz's increments and a class of the lag increments are the special cases of this general form of increments. Our results imply the theorem that have been given by Csorgo and Revesz (1978), and some of their conditions are removed.展开更多
We introduce anticipating quadrant and symmetric integrals in the plane, and establish the associated chain rules which are the same as the deterministic ones. In particular, we deduce the relation between quadrant in...We introduce anticipating quadrant and symmetric integrals in the plane, and establish the associated chain rules which are the same as the deterministic ones. In particular, we deduce the relation between quadrant integrals, symmetric integral, and Skorohod integral with respect to two-parameter Wiener processes.展开更多
The purpose of this paper is to investigate the behavior of a Wiener integral along the curve C of the scale factor ρ > 0 for the Wiener integral ∫C0[0,T]F(ρx)dm(x) about the function defined on the Wiener space...The purpose of this paper is to investigate the behavior of a Wiener integral along the curve C of the scale factor ρ > 0 for the Wiener integral ∫C0[0,T]F(ρx)dm(x) about the function defined on the Wiener space C0[0,T], where θ(t,u) is a Fourier-Stieltjes transform of a complex Borel measure.展开更多
In this paper, we discuss the average errors of function approximation by linear combinations of Bernstein operators. The strongly asymptotic orders for the average errors of the combinations of Bernstein operators se...In this paper, we discuss the average errors of function approximation by linear combinations of Bernstein operators. The strongly asymptotic orders for the average errors of the combinations of Bernstein operators sequence are determined on the Wiener space.展开更多
基金Supported by the National Natural Science Foundation of ChinaZhejiang Province Natural Science Fund
文摘In this paper, we consider a general form of the increments for a two-parameter Wiener process. Both the Csorgo-Revesz's increments and a class of the lag increments are the special cases of this general form of increments. Our results imply the theorem that have been given by Csorgo and Revesz (1978), and some of their conditions are removed.
文摘We introduce anticipating quadrant and symmetric integrals in the plane, and establish the associated chain rules which are the same as the deterministic ones. In particular, we deduce the relation between quadrant integrals, symmetric integral, and Skorohod integral with respect to two-parameter Wiener processes.
文摘The purpose of this paper is to investigate the behavior of a Wiener integral along the curve C of the scale factor ρ > 0 for the Wiener integral ∫C0[0,T]F(ρx)dm(x) about the function defined on the Wiener space C0[0,T], where θ(t,u) is a Fourier-Stieltjes transform of a complex Borel measure.
文摘In this paper, we discuss the average errors of function approximation by linear combinations of Bernstein operators. The strongly asymptotic orders for the average errors of the combinations of Bernstein operators sequence are determined on the Wiener space.
