论文标题
通用Mehler Semigroups的时间规律性
Time regularity for generalized Mehler semigroups
论文作者
论文摘要
我们研究了$ t \ mapsto p_tf $的连续性和Hölder连续性，其中$ p_t $是$ c_b（x）$的概括的Mehler Semigroup，这是从Banach Space $ x $到$ r $的连续和有限函数的空间，以及$ f \ in C_B（x）$。此类半群的发电机$ l $是对有限和无限维度的一类差分和伪差异操作员的实现。该理论适用的运算符$ l $的示例包括有限维度中具有分数扩散的Ornstein-Uhlenbeck运算符，以及无限的尺寸的Ornstein-Uhlenbeck Operators，具有相关的强细胞群。
We study continuity and Hölder continuity of $t\mapsto P_tf$, where $P_t$ is a generalized Mehler semigroup in $C_b(X)$, the space of the continuous and bounded functions from a Banach space $X$ to $R$, and $f\in C_b(X)$. The generators $L$ of such semigroups are realizations of a class of differential and pseudo-differential operators, both in finite and in infinite dimension. Examples of operators $L$ to which this theory is applicable include Ornstein-Uhlenbeck operators with fractional diffusion in finite dimension, and Ornstein-Uhlenbeck operators with associated strong-Feller semigroups, in infinite dimension.
