Inference for Gamma and Stable Processes

Abstract

Problems of estimation and testing for nondecreasing pure jump gamma and stable additive processes are considered. The inference is based on a single realization of the process on a given time interval [0,t]. The maximum likelihood estimators of the parameters based on observation of the jumps of size greater than or equal to ε are found to be consistent as ε tends to 0 for the stable process but not for the gamma process.

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