论文标题
马尔可夫流程的迭代对数的一般法律：liminf法律
General Law of iterated logarithm for Markov processes: Liminf laws
论文作者
论文摘要
从Arxiv继续：2102.01917V2，在本文中，我们讨论了迭代对数（LIL）的一般标准和形式，以进行连续的马尔可夫过程。在一些最小的假设下，比Arxiv中的假设弱：2102.01917V2，我们在一般度量度量空间中以零（分别为Infinity）建立Liminf LIL。特别是，我们对LIMF定律在零时的假设，而Liminf Lil的形式确实是局部的，因此我们可以涵盖高度空间的构成病例。我们的结果涵盖了ARXIV中的所有示例：2102.01917V2，包括具有远距离跳跃的随机电导模型。此外，我们表明，LIL的LIMINF定律的一般形式对于一大批跳跃过程而言，其跳跃措施具有对数尾巴和flyer尾的过程，并具有不同顺序的符号，而订单的符号则没有涵盖。
Continuing from arXiv:2102.01917v2, in this paper, we discuss general criteria and forms of liminf laws of iterated logarithm (LIL) for continuous-time Markov processes. Under some minimal assumptions, which are weaker than those in arXiv:2102.01917v2, we establish liminf LIL at zero (at infinity, respectively) in general metric measure spaces. In particular, our assumptions for liminf law of LIL at zero and the form of liminf LIL are truly local so that we can cover highly space-inhomogenous cases. Our results cover all examples in arXiv:2102.01917v2 including random conductance models with long range jumps. Moreover, we show that the general form of liminf law of LIL at zero holds for a large class of jump processes whose jumping measures have logarithmic tails and Feller processes with symbols of varying order which are not covered before.
