In this paper we present a general mathematical construction that allows usto define a parametric class of $H$-sssi stochastic processes (self-similarwith stationary increments), which have marginal probability density functionthat evolves in time according to a partial integro-differential equation offractional type. This construction is based on the theory of finite measures onfunctional spaces. Since the variance evolves in time as a power function,these $H$-sssi processes naturally provide models for slow and fast anomalousdiffusion. Such a class includes, as particular cases, fractional Brownianmotion, grey Brownian motion and Brownian motion.
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机译：在本文中，我们提出了一种通用的数学构造，该构造允许我们定义$ H $ -sssi随机过程（自相似与平稳增量）的参数类，其具有根据部分积分微分方程随时间变化的边际概率密度函数。类型。该构造基于功能空间的有限度量理论。由于方差作为幂函数随时间变化，因此这些$ H $ -sssi流程自然会提供慢速和快速异常扩散的模型。在特定情况下，此类包括分数布朗运动，灰色布朗运动和布朗运动。
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