Existence
If then satisfies the conditions i)–iii). Otherwise, in the case of finite measure, given, a Poisson random variable with rate, and, mutually independent random variables with distribution, define where is a degenerate measure located in . Then will be a Poisson random measure. In the case is not finite the measure can be obtained from the measures constructed above on parts of where is finite.
Read more about this topic: Poisson Random Measure
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