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

H. Wang and X. Chen

Statistics & Probability Letters, 1997, vol. 33, issue 1, 79-84

Abstract: Let X(N,d) be a N-parameter Omstein-Uhlenbeck process taking values in ##R##d. In this paper, we prove that, for an arbitrary pair of positive integers (N, d) and any open set S in ##R##d, X(N,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 ##R##d which is interval recurrent only for the positive integer pairs (N, d) d [less-than-or-equals, slant] 2N.

Keywords: (N; d)-Wiener process (N; d)-Ornstein-Uhlenbeck processes Recurrence Transience (search for similar items in EconPapers)
Date: 1997
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