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

Abstract

This paper is concerned with various aspects of the Slepian process $(B_{t+1}-B_t,t\ge 0)$ derived from a one-dimensional Brownian motion $(B_t,t\ge 0)$. 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 $0\le t\le 1$. 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 $(B_{T+u}-B_T,0\le u\le 1)$ is standard Brownian bridge.

28 pages, 3 figures and 3 tables. This paper is published by http://ejp.ejpecp.org/article/view/3911

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Cited by in corpus (2)

• The Slepian zero set, and Brownian bridge embedded in Brownian motion by a spacetime shift
• Construction and Characterisation of Stationary and Mass-Stationary Random Measures on ${\mathbb{R}}^d$