It is well-known that compositions of Markov processes with inverse subordinators are governed by integro-differential equations of generalized fractional type. This kind of processes are of wide interest in statistical physics as they are connected to anomalous diffusions. In this paper we consider a generalization; more precisely we mean componentwise compositions of $\mathbb{R}^d$-valued Markov processes with the components of an independent multivariate inverse subordinator. As a possible application, we present a model of anomalous diffusion in anisotropic medium, which is obtained as a weak limit of suitable continuous-time random walks.

中文翻译：

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具有多元从属项逆的随机时间变化：控制方程和分数动力学

众所周知，具有逆从属项的马尔可夫过程的组合由广义分数型的积分微分方程控制。这种过程在统计物理学中具有广泛的兴趣，因为它们与异常扩散有关。在本文中，我们考虑一个概括；更准确地说，我们指的是 $\mathbb{R}^d$-valued Markov 过程与独立多元逆从属项的组件的组件组合。作为一个可能的应用，我们提出了一个各向异性介质中的异常扩散模型，它是作为合适的连续时间随机游走的弱极限获得的。