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The Joint Distribution of Running Maximum of a Slepian Process

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  • Pingjin Deng

    (Nankai University
    University of Lausanne)

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

Suggested Citation

  • Pingjin Deng, 2018. "The Joint Distribution of Running Maximum of a Slepian Process," Methodology and Computing in Applied Probability, Springer, vol. 20(4), pages 1123-1135, December.
    • Handle: RePEc:spr:metcap:v:20:y:2018:i:4:d:10.1007_s11009-017-9594-z
    DOI: 10.1007/s11009-017-9594-z
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    References listed on IDEAS

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