论文标题
多局部多稳定Riemann-Liouville流程的小波系列表示
Wavelet series representation for multifractional multistable Riemann-Liouville process
论文作者
论文摘要
本文的主要目的是为随机字段$ x $构建小波型随机串联表示，该表示由多稳定随机积分定义，该积分生成了多效性多效性Riemann-Liouville（MMRL）流程$ y $。除其他外，这种表示提供了$ y $的路径的有效方法。为了获得它，我们在HAAR基础上扩展了与$ x $相关的集成，我们使用了多稳态随机积分的一些基本属性。然后，由于亚伯的求和规则和DOOB对离散的非平滑赛的最大不等式，我们表明，$ x $的小波型随机串联表示在很强的意义上是融合的：在连续功能的某些空间中，几乎可以肯定。另外，我们确定了其在这些空间中几乎确定的收敛速率的估计。
The main goal of this paper is to construct a wavelet-type random series representation for a random field $X$, defined by a multistable stochastic integral, which generates a multifractional multistable Riemann-Liouville (mmRL) process $Y$. Such a representation provides, among other things, an efficient method of simulation of paths of $Y$. In order to obtain it, we expand in the Haar basis the integrand associated with $X$ and we use some fundamental properties of multistable stochastic integrals. Then, thanks to the Abel's summation rule and the Doob's maximal inequality for discrete submartingales, we show that this wavelet-type random series representation of $X$ is convergent in a strong sense: almost surely in some spaces of continuous functions. Also, we determine an estimate of its almost sure rate of convergence in these spaces.
