REGULARITY OF 1(P)-VALUED ORNSTEIN-UHLENBECK RANDOM FUNCTIONS WHERE P IS-AN-ELEMENT-OF [1, INFINITY]

• 成果类型: Article
• 署名作者: FERNIQUE, X
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176989699
• 发表日期: 1992
• 页码: 1441-1449
• 关键词: continuity

摘要

In this note, we study the regularity of R(N)-valued random functions X = (X(n), n is-an-element-of N) on R such that X(n)(t) = a(n)x(n)(b(n)t), t is-an-element-of R, n is-an-element-of N, where a = (a(n)) subset-of R+, b = (b(n)) subset-of R+ and (X(n), n is-an-element-of N) is an i.i.d. sequence of gaussian centered stationary real random functions on R. If the common covariance of the x(n)'s verifies some very weak regularity assumptions, then their paths are continuous in l(p), p is-an-element-of [1, infinity[ if and only if they are in this space and some integral depending uniquely on p and on a and b is convergent. These results extend and refine some previous results concerning only the case p is-an-element-of [2, infinity[.