Besov空间中双参数Volterra型重分数过程的弱逼近
Weak Convergence to the Two-Parameter Volterra Multifractional Process in Besov Spaces

DOI：10.3770/j.issn:2095-2651.2017.05.012

 作者 单位 刘俊峰 南京审计大学统计学系, 江苏 南京 211815 孙西超 蚌埠学院数学物理系, 安徽 蚌埠 233030

本文中,通过构造如下的随机过程序列$$B_{n}(s,t)=\int_{0}^{s}\int_{0}^{t}K_{\alpha(s)}(s,u)K_{\beta(t)}(t,v)\theta_{n}(u,v)\d u\d v,$$ 其中随机过程$\theta_{n}(u,v)$在$n\in \mathbb{N}$时依分布收敛至布朗单.我们主要证明当$n\rightarrow\infty$时,序列$B_n(s,t)$在各向异性Besov空间依分布收敛到双参数Volterra型重分数过程.

In this paper, we prove that two-parameter Volterra multifractional process can be approximated in law in the topology of the anisotropic Besov spaces by the family of processes $\{B_{n}(s,t)\}_{n\in \mathbb{N}}$ defined by $$B_{n}(s,t)=\int_{0}^{s}\int_{0}^{t}K_{\alpha(s)}(s,u)K_{\beta(t)}(t,v)\theta_{n}(u,v)\d u\d v,$$ where $\{\theta_{n}(u,v)\}_{n\in \mathbb{N}}$ is a family of processes, converging in law to a Brownian sheet as $n\rightarrow\infty$, based on the well known Donsker's theorem.