Recurrent extensions of self-similar Markov processes and Cramér’s condition II
Recurrent extensions of self-similar Markov processes and Cramér’s condition II
复制标题
自相似马尔可夫过程和克拉梅尔条件 II 的循环扩展
DOI：
10.3150/bj/1120591185
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发表时间：
2005
期刊：
影响因子：
1.5
通讯作者：
V. Rivero
中科院分区：
文献类型：
--
作者：
V. Rivero
设P=(Fx，x>；0)是Skohorod空间D+上的一族概率测度族，D+是定义在[0，0，Of]上且值在R+中的CADLAG路径空间。空间D+具有Skohorod拓扑及其Borel a-域。我们用X表示坐标的正则过程，(Qt，t>；0)将是由X生成的自然滤子。假设在P下，正则过程X是正的自相似马尔可夫过程(PsMp)。也就是说，(X，P)是具有如下标度性质的[0，00]值强马尔可夫过程：存在a>；0使得对于每个c>；0，
Let P = (Fx, x > 0) be a family of probability measures on Skohorod's space D+, the space of cadlag paths defined on [0, oof with values in R+. The space D+ is endowed with the Skohorod topology and its Borel a-field. We will denote by X the canonical process of the coordinates and (Qt, t > 0) will be the natural filtration generated by X. Assume that under P the canonical process X is a positive self-similar Markov process (pssMp). That is, (X, P) is a [0, oo [-valued strong Markov process with the following scaling property: there exists an a > 0 such that for every c > 0,