ISSN:
1432-2064
Keywords:
60 J 25
;
60 J 45
;
60 G 57
;
60 J 60
;
60 J 80
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Summary Let (ξ s ) be a continuous Markov process satisfying certain regularity assumptions. We introduce a path-valued strong Markov process associated with (ξ s ), which is closely related to the so-called superprocess with spatial motion (ξ s ). In particular, a subsetH of the state space of (ξ s ) intersects the range of the superprocess if and only if the set of paths that hitH 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 (ξ s ) is a diffusion process, we recover certain results recently obtained by Dynkin.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01197336
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