Compound Poisson Process

  Poisson process
A compound Poisson process with rate \lambda>0 and jump size distribution G is a parametrized family y = \{\,Y(t) : t \geq 0 \,\} of random variables given by
Y(t) = \sum_{i=1}^{N(t)} D_i
where,
\{\,N(t) : t \geq 0\,\} is a Poisson process with rate \lambda, and \{\,D_i : i \geq 0\,\} are independent and identically distributed random variables, with distribution function G, which are also independent of \{\,N(t) : t \geq 0\,\}.\,

 

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