Abstract
LetX be a strongly symmetric standard Markov process on a locally compact metric spaceS with 1-potential densityu 1(x, y). Let {L yt , (t, y)∈R +×S} denote the local times ofX and letG={G(y), y∈S} be a mean zero Gaussian process with covarianceu 1(x, y). In this paper results about the moduli of continuity ofG are carried over to give similar moduli of continuity results aboutL yt considered as a function ofy. Several examples are given with particular attention paid to symmetric Lévy processes.
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The research of both authors was supported in part by a grant from the National Science Foundation. In addition the research of Professor Rosen was also supported in part by a PSC-CUNY research grant. Professor Rosen would like to thank the Israel Institute of Technology, where he spent the academic year 1989–90 and was supported, in part, by the United States-Israel Binational Science Foundation. Professor Marcus was a faculty member at Texas A&M University while some of this research was carried out.
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Marcus, M.B., Rosen, J. Moduli of continuity of local times of strongly symmetric Markov processes via Gaussian processes. J Theor Probab 5, 791–825 (1992). https://doi.org/10.1007/BF01058730
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DOI: https://doi.org/10.1007/BF01058730