On the interval recurrence property of (N, d)-Ornstein-Uhlenbeck processes

✍ Scribed by H. Wang; X. Chen

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 274 KB
• Volume: 33
• Category: Article
• ISSN: 0167-7152
• DOI: 10.1016/s0167-7152(96)00112-5

✦ Synopsis

Let X (N'd) be a N-parameter Omstein-Uhlenbeck process taking values in ~a. In this paper, we prove that, for an arbitrary pair of positive integers (N, d) and any open set S in R d, X (u'd) is recurrent to S. This is surprisingly different from the recurrence properties of the N-parameter Wiener process W (N'd) taking values in N d which is interval recurrent only for the positive integer pairs (N, d) with d ~<2N.