论文标题
一些与多参数Lévy过程有关的随机领域的家庭
Some families of random fields related to multiparameter Lévy processes
论文作者
论文摘要
令$ \ mathbb {r}^n _+= [0，\ infty）^n $。我们在这里考虑一类随机字段$（x_t）_ {t \ in \ mathbb {r}^n _+} $，称为多参数lévy流程。相关的操作员及其发电机的多参数半群代表伪差异操作员。我们还通过所谓的下属字段来考虑$（x_t）_ {t \ in \ mathbb {r}^n _+} $的组成，我们提供了菲利普斯公式。我们最终通过所谓的逆随机字段来研究$（x_t）_ {t \ in \ mathbb {r}^n _+} $的组成，这产生了有趣的长距离依赖性属性。作为我们分析的副产品，我们研究了一种在各向异性介质中扩展的异常扩散模型，该模型扩展了[8]中治疗的一种。
Let $\mathbb{R}^N_+= [0,\infty)^N$. We here consider a class of random fields $(X_t)_{t\in \mathbb{R}^N_+}$ which are known as Multiparameter Lévy processes. Related multiparameter semigroups of operators and their generators are represented as pseudo-differential operators. We also consider the composition of $(X_t)_{t\in \mathbb{R}^N_+}$ by means of the so-called subordinator fields and we provide a Phillips formula. We finally study the composition of $(X_t)_{t\in \mathbb{R}^N_+}$ by means of the so-called inverse random fields, which gives rise to interesting long range dependence properties. As a byproduct of our analysis, we study a model of anomalous diffusion in an anisotropic medium which extends the one treated in [8].
