Let Ni Ni (t ), t 0 , i 1, 2, be nonhomogeneous Poisson processes with respective intensity functions i (t ), i 1, 2 Suppose 1(t) 2(t) for all t Let Aj , j 1, , n be arbitrary subsets of the real line, and for i 1, 2, let Ni(Aj ) be the number of points of the process Ni that are in Aj , j 1, , n S...

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Let Ni = {Ni (t ), t 0}, i = 1, 2, be nonhomogeneous Poisson processes

Question:

Let Ni = {Ni (t ), t ≥ 0}, i = 1, 2, be nonhomogeneous Poisson processes with respective intensity functions λi (t ), i = 1, 2. Suppose λ1(t) ≥ λ2(t) for all t .

Let Aj , j = 1, . . . , n be arbitrary subsets of the real line, and for i = 1, 2, let Ni(Aj ) be the number of points of the process Ni that are in Aj , j = 1, . . . , n.

Show that (N1(A1), . . . , N1(An)) ≥st (N2(A1), . . . , N2(An)).

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