The Joint Distribution of Running Maximum of a Slepian Process

Pingjin Deng ()
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Pingjin Deng: Nankai University

Methodology and Computing in Applied Probability, 2018, vol. 20, issue 4, 1123-1135

Abstract: Abstract Consider the Slepian process S defined by S(t) = B(t + 1) − B(t),t ∈ [0, 1] with B(t), t ∈ ℝ a standard Brownian motion. In this contribution we analyze the properties between the maximum m s = max 0 ≤ u ≤ s S ( u ) $m_{s}=\max \limits _{0\leq u\leq s}S(u)$ and the maximum m t = max 0 ≤ u ≤ t S ( u ) $m_{t}=\max \limits _{0\leq u\leq t}S(u)$ for 0 ≤ s

Keywords: Gaussian processes; Slepian processes; Running maximum; 60G15; 60G70 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s11009-017-9594-z

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