Open AccessQuasi-likelihood Estimation in Fractional Levy SPDEs from Poisson Sampling
Author(s) -
Jaya P. N. Bishwal
Publication year - 2022
Publication title -
european journal of mathematical analysis
Language(s) - English
Resource type - Journals
ISSN - 2733-3957
DOI - 10.28924/ada/ma.2.15
Subject(s) - mathematics , estimator , consistency (knowledge bases) , poisson distribution , asymptotic distribution , compound poisson process , estimation theory , strong consistency , lévy process , quasi likelihood , stochastic differential equation , statistics , poisson process , count data , geometry
We study the quasi-likelihood estimator of the drift parameter in the stochastic partial differential equations driven by a cylindrical fractional Levy process when the process is observed at the arrival times of a Poisson process. We use a two stage estimation procedure. We first estimate the intensity of the Poisson process. Then we plug-in this estimate in the quasi-likelihood to estimate the drift parameter. We obtain the strong consistency and the asymptotic normality of the estimators.