A Poisson process on metric space is introduced and some of the properties of the stochastic integral with respect to this process are described. This integral allows us to define the likelihood ratio formula and to derive certain useful inequalities for the moments of likelihood ratio. Supposing that the intensity function of the Poisson process depends on the unknown finite-dimensional parameter, we define the maximum likelihood, Bayes, and minimum distance estimators of this parameter and give the first examples of these estimators.
KeywordsPoisson Process Fisher Information Intensity Function Mathematical Expectation Auxiliary Result
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