Lévy processes | Poisson point processes

Compound Poisson process

A compound Poisson process is a continuous-time (random) 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. A compound Poisson process, parameterised by a rate and jump size distribution G, is a process given by where, is a counting of a Poisson process with rate , and are independent and identically distributed random variables, with distribution function G, which are also independent of When are non-negative integer-valued random variables, then this compound Poisson process is known as a stuttering Poisson process which has the feature that two or more events occur in a very short time . (Wikipedia).

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Related pages

Borel set | Law of total variance | Variance | Convergence of random variables | Law of total probability | Expected value | Compound Poisson distribution | Wald's equation | Real number | Probability distribution | Poisson distribution | Stochastic process | Convolution