The Slepian zero set, and Brownian bridge embedded in Brownian motion by a spacetime shift
نویسندگان
چکیده
This paper is concerned with various aspects of the Slepian process (Bt+1 −Bt, t ≥ 0) derived from one-dimensional standard Brownian motion (Bt, t ≥ 0). In particular, we offer an analysis of the local structure of the Slepian zero set {t : Bt+1 = Bt}, including a path decomposition of the Slepian process for 0 ≤ t ≤ 1. We also establish the existence of a random time T ≥ 0 such that the process (BT+u −BT , 0 ≤ u ≤ 1) is standard Brownian bridge.
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