A time-changed fractional mixed fractional Brownian motion by inverse alpha stable subordinator with index alpha in (0, 1) is an iterated process L constructed as the superposition of fractional mixed fractional Brownian motion N(a, b) and an independent inverse {\alpha}-stable subordinator Talpha. In this paper we prove that the process LT alpha(a, b) is of long range dependence property under a smooth condition on the Hirsh index H1 and H2. We deduce that the fractional mixed fractional Brownian motion has long range dependence for every H1 < H2.

翻译：时间变化的分数混合分数布朗运动由反阿尔法稳定分管和指数阿尔法(0,1)的反阿尔法稳定分管组成,是一个迭代过程L,是分分管混合分管Brown运动N(a,b)的叠加,是独立的倒数分管分管分管Talpha。在本文中,我们证明,在Hirsh指数H1和H2的平稳条件下,ALT(a,b)的过程具有长程依赖性。 我们推断,分管混合分管布朗尼运动对每1 < H2的H1 < H2具有长期依赖性。