The joint distributions of running maximum of a Slepian processes

الأصل · EN

Consider the Slepian process S defined by S(t)=B(t+1)-B(t),t∈ [0,1] with B(t),t∈ a standard Brownian motion.In this contribution we analyze the joint distribution between the maximum mₛ=₀≤ ᵤ≤ ₛS(u) certain and the maximum Mₜ=₀≤ ᵤ≤ ₜS(u) for 0< s < t fixed. Explicit integral expression are obtained for the distribution function of the partial maximum mₛ and the joint distribution function between mₛ and Mₜ. We also use our results to determine the moments of mₛ.