LAN property for an ergodic diffusion with jumps
Arturo Kohatsu-Higa, Eulalia Nualart, Ngoc Khue Tran
TL;DR
This paper establishes the LAN property for a multidimensional ergodic diffusion with jumps, observed at high frequency, where the drift depends on an unknown parameter, aiding statistical inference.
Contribution
It proves the LAN property for a class of jump-diffusions with finite Lévy measure, extending existing results to more complex stochastic processes.
Findings
LAN property derived for the process
Facilitates statistical inference for the unknown parameter
Applicable to high-frequency discrete observations
Abstract
In this paper, we consider a multidimensional ergodic diffusion with jumps driven by a Brownian motion and a Poisson random measure associated with a pure-jump L\'evy process with finite L\'evy measure, whose drift coefficient depends on an unknown parameter. Considering the process discretely observed at high frequency, we derive the local asymptotic normality (LAN) property.
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Taxonomy
TopicsStochastic processes and financial applications · Stochastic processes and statistical mechanics · Statistical Methods and Inference