Compound Poisson process

Definition

Let Failed to parse (Conversion error. Server ("/media/api/rest_") reported: "Cannot get mml. TeX parse error: Undefined control sequence \emph"): {\displaystyle {\emph {y}}=\{Y(t),t\geq 0\}} be a Compound Poisson Process with rate $\lambda$ and jump size distribution G.

Then,
$Y(t)=\sum _{i=1}^{N(t)}D_{i},t\geq 0$

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 ${N(t),t\geq 0}$