Gamma process

A gamma process is a random process with independent gamma distributed increments. Often written as ${\displaystyle \Gamma (t;\gamma ,\lambda )}$, it is a pure-jump increasing Lévy process with intensity measure ${\displaystyle \nu (x)=\gamma x^{-1}\exp(-\lambda x)}$, for positive ${\displaystyle x}$. Thus jumps whose size lies in the interval ${\displaystyle [x,x+dx)}$ occur as a Poisson process with intensity ${\displaystyle \nu (x)dx.}$ The parameter ${\displaystyle \gamma }$ controls the rate of jump arrivals and the scaling parameter ${\displaystyle \lambda }$ inversely controls the jump size. It is assumed that the process starts from a value 0 at t=0.

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