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Some basic properties of the gamma process are:{{citation needed|date=February 2012}}
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The [[marginal distribution]] of a gamma process at time <math>t</math> is a [[gamma distribution]] with mean <math>\gamma t/\lambda</math> and variance <math>\gamma t/\lambda^2.</math>
That is, its density <math>f</math> is given by <math display="block">f(x;t, \gamma, \lambda) = {\frac {\lambda ^{\gamma t}}{\Gamma (\gamma t)}}x^{\gamma t \,-\,1}e^{-\lambda x}.</math>
=== scaling ===▼
Multiplication of a gamma process by a scalar constant <math>\alpha</math> is again a gamma process with different mean increase rate.
:<math>\alpha\Gamma(t;\gamma,\lambda) \simeq \Gamma(t;\gamma,\lambda/\alpha)\,</math>
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The sum of two independent gamma processes is again a gamma process.
:<math>\Gamma(t;\gamma_1,\lambda) + \Gamma(t;\gamma_2,\lambda) \simeq \Gamma(t;\gamma_1+\gamma_2,\lambda)\,</math>
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:<math>\mathbb{E}(X_t^n) = \lambda^{-n}\Gamma(\gamma t+n)/\Gamma(\gamma t),\ \quad n\geq 0 ,</math> where <math>\Gamma(z)</math> is the [[Gamma function]].
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:<math>\mathbb{E}\Big(\exp(\theta X_t)\Big) = (1-\theta/\lambda)^{-\gamma t},\ \quad \theta<\lambda</math>
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:<math>\operatorname{Corr}(X_s, X_t) = \sqrt{s/t},\ s<t</math>, for any gamma process <math>X(t) .</math>
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