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In mathematics and probability theory, a gamma process, also known as Gamma subordinator, is a random process with independent gamma distributed increments. Often written as Γ {\displaystyle \Gamma } , it is a pure-jump increasing Lévy process with intensity measure ν = γ x − 1 exp , {\displaystyle \nu =\gamma x^{-1}\exp,} for positive x {\displaystyle x} . Thus jumps whose size lies in the interval {\displaystyle } occur as a Poisson process with intensity ν d x . {\displaystyle \nu \,dx.} The parameter γ {\displaystyle \gamma } controls the rate of jump arrivals and the scaling parameter λ {\displaystyle \lambda } inversely controls the jump size. It is assumed that the process starts from a value 0 at t = 0.
The gamma process is sometimes also parameterised in terms of the mean and variance of the increase per unit time, which is equivalent to γ = μ 2 / v {\displaystyle \gamma =\mu ^{2}/v} and λ = μ / v {\displaystyle \lambda =\mu /v} .