Local nondeterminism and local times for stable processes View Full Text


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Article Info

DATE

1989-08

AUTHORS

John P. Nolan

ABSTRACT

Our main theorem gives sufficient conditions for symmetric stable processes and fields to have a jointly continuous local time. The approach is through the Lp representation for such processes. We develop a measure of dependence for vectors in a normed linear space and use that to analyze the probabilistic independence of the increments of a stable process. Local nondeterminism is defined for stable processes and shown to be equivalent to “locally approximately independent increments.” Sufficient conditions for several classes of stable processes to be local nondeterministic are given. These ideas are extended to multidimensional stable random fields and we prove existence of jointly continuous local times. The results extend most Gaussian results to their stable analogs. More... »

PAGES

387-410

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/bf00339994

DOI

http://dx.doi.org/10.1007/bf00339994

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1025565786


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