Generalized Mehler semigroups:: The non-Gaussian case

被引：50
|
作者：
Fuhrman, M
Röckner, M
机构：
[1] Politecn Milan, Dipartimento Matemat, I-20133 Milan, Italy
[2] Univ Bielefeld, Fak Math, D-33501 Bielefeld, Germany
来源：
POTENTIAL ANALYSIS | 2000年 / 12卷 / 01期
关键词：
Markovian semigroups; Mehler formula; cadlag processes in abstract spaces; tightness of capacities;
D O I：
10.1023/A:1008644017078
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study generalized Mehler semigroups, introduced in [7], with special emphasis on the non-Gaussian case. We review and simplify the method of construction. In the general (non-Gaussian) case we construct an associated cadlag Markov process in an appropriate state space obtained as a solution of a stochastic equation which can be solved 'omega by omega'. We also show tightness of the associated (r, p)-capacities. Invariant measures, time regularity and a definition of the generator are also studied.
引用
收藏
页码：1 / 47
页数：47
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