论文标题
无限尺寸空间中的非高斯措施：伽玛 - 灰噪声
Non-Gaussian Measures in Infinite Dimensional Spaces: the Gamma-Grey Noise
论文作者
论文摘要
在非高斯分析的背景下，Schneider [27]引入了基于Mittag-Leffler功能的灰噪声度量。类似地，构建了灰色的布朗尼运动及其概括（例如，参见[25]，[6]，[7]，[8]）。在本文中，我们通过不完整的伽马功能（利用其完全的单调性）来构建和研究一种新的非高斯措施。我们将此度量标记为γ-灰噪声，并证明了Appell系统的存在。在无限尺寸环境中，相关的广义过程也是定义的，并通过使用Riemann-Liouville分数操作员，因此引入了（可能是缓和的）Gamma-Grey Brownian运动。还提供了这些过程的许多不同特征，以及通过其过渡密度满足的整数差异方程。它们允许对异常扩散进行建模，模仿经典随机演算的过程。
In the context of non-Gaussian analysis, Schneider [27] introduced grey noise measures, built upon Mittag-Leffler functions; analogously, grey Brownian motion and its generalizations were constructed (see, for example, [25], [6], [7], [8]). In this paper, we construct and study a new non-Gaussian measure, by means of the incomplete-gamma function (exploiting its complete monotonicity). We label this measure Gamma-grey noise and we prove, for it, the existence of Appell system. The related generalized processes, in the infinite dimensional setting, are also defined and, through the use of the Riemann-Liouville fractional operators, the (possibly tempered) Gamma-grey Brownian motion is consequently introduced. A number of different characterizations of these processes are also provided, together with the integro-differential equation satisfied by their transition densities. They allow to model anomalous diffusions, mimicking the procedures of classical stochastic calculus.
