The Slepian zero set, and Brownian bridge embedded in Brownian motion by a spacetime shift

This paper is concerned with various aspects of the Slepian process $(B_{t+1}

B_t, t \ge 0) $d e r i v e d f r o m a o n e - d i m e n s i o n a l B r o w n i a n m o t i o n$ (B_t, t \ge 0 )$. In particular, we offer an analysis of the local structure of the Slepian zero set ${t : B_{t + 1} = B_{t}}$ , including a path decomposition of the Slepian process for $0 \leq t \leq 1$ . We also establish the existence of a random time $T$ such that $T$ falls in the the Slepian zero set almost surely and the process $(B_{T + u} - B_{T}, 0 \leq u \leq 1)$ is standard Brownian bridge.

This paper is concerned with various aspects of the Slepian process $(B_{t+1}

B_t, t \ge 0) $d e r i v e d f r o m a o n e - d i m e n s i o n a l B r o w n i a n m o t i o n$ (B_t, t \ge 0 )$. In particular, we offer an analysis of the local structure of the Slepian zero set ${t : B_{t + 1} = B_{t}}$ , including a path decomposition of the Slepian process for $0 \leq t \leq 1$ . We also establish the existence of a random time $T$ such that $T$ falls in the the Slepian zero set almost surely and the process $(B_{T + u} - B_{T}, 0 \leq u \leq 1)$ is standard Brownian bridge.

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