SELF-INTERSECTIONS AND LOCAL NONDETERMINISM OF GAUSSIAN-PROCESSES

• 成果类型: Article
• 署名作者: BERMAN, SM
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176990539
• 发表日期: 1991
• 页码: 160-191
• 关键词: FIELDS; times

摘要

Let X(t), t greater-than-or-equal-to 0, be a vector Gaussian process in R(m) whose components are i.i.d. copies of a real Gaussian process X(t) with stationary increments. Under specified conditions on the spectral distribution function used in the representation of the incremental variance function, it is shown that the self-intersection local time of multiplicity r of the vector process is jointly continuous. The dimension of the self-intersection set is estimated from above and below. The main tool is the concept of local nondeterminism.