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{{Short description|Random process in probability theory}}
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A '''compound Poisson process''' is a continuous-time [[stochastic process]] with jumps. The jumps arrive randomly according to a [[Poisson process]] and the size of the jumps is also random, with a specified probability distribution. To be precise, a compound Poisson process, parameterised by a rate <math>\lambda > 0</math> and jump size distribution ''G'', is a process <math>\{\,Y(t) : t \geq 0 \,\}</math> given by
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