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The Poisson process. I1, I2, . . . , Im, . . .
 

Summary: The Poisson process.
Let
I1, I2, . . . , Im, . . .
be a sequence of independent identically distributed continuous random variables. Let T0 = 0 and, for each
positive integer m, let
Tm =
m
i=0
Ii.
Evidently,
0 = T0 < T1 < < Tm < .
For nonnegative integers m, n with m n let
Tm,n =
m Ii;
note that
Tn = Tm + Tm,n;
and that
Tm,n and Tm-n have the same distribution, which is to say that fTm,n = fTm-n .
Let F : R [0, 1] be such that

  

Source: Allard, William K. - Department of Mathematics, Duke University

 

Collections: Mathematics