A CLASS OF PATH-VALUED MARKOV-PROCESSES AND ITS APPLICATIONS TO SUPERPROCESSES

被引:70
作者
LEGALL, JF
机构
[1] Laboratoire de Probabilités, Université Paris VI, Paris Cedex 05, F-75252, 4 Place Jussieu
关键词
D O I
10.1007/BF01197336
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
Let (xi(S)) be a continuous Markov process satisfying certain regularity assumptions. We introduce a path-valued strong Markov process associated with (xi(S)), which is closely related to the so-called superprocess with spatial motion (xi(S)). In particular, a subset H of the state space of (xi(S)) intersects the range of the superprocess if and only if the set of paths that hit H is not polar for the path-valued process. The latter property can be investigated using the tools of the potential theory of symmetric Markov processes: A set is not polar if and only if it supports a measure of finite energy. The same approach can be applied to study sets that are polar for the graph of the superprocess. In the special case when (xi(S)) is a diffusion process, we recover certain results recently obtained by Dynkin.
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页码:25 / 46
页数:22
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