P-VARIATION OF THE LOCAL-TIMES OF SYMMETRICAL STABLE PROCESSES AND OF GAUSSIAN-PROCESSES WITH STATIONARY INCREMENTS
成果类型：
Article
署名作者：
MARCUS, MB; ROSEN, J
署名单位：
Texas A&M University System; Texas A&M University College Station; City University of New York (CUNY) System; College of Staten Island (CUNY)
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/aop/1176989525
发表日期：
1992
页码：
1685-1713
关键词：
摘要：
Let {L(t)x, (t, x) is-an-element-of R+ X T} be the local time of a real-valued symmetric stable process of order 1 < beta less-than-or-equal-to 2 and let {pi(n)} be a sequence of partitions of [0, a]. Results are obtained for [GRAPHICS] both almost surely and in L(r) for all r > 0. Results are also obtained for a similar expression but where the supremum of the sum is taken over all partitions of [0, a] and a function other than a power is applied to the increments of the local times. The proofs use a lemma of the authors' which is a consequence of an isomorphism theorem of Dynkin and which relates sample path behavior of local times with those of associated Gaussian processes. The major effort in this paper consists of obtaining results on the p-variation of the associated Gaussian processes. These results are of independent interest since the associated processes include fractional Brownian motion.
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