Threshold estimation for jump-diffusions under small noise asymptotics

Mitsuki Kobayashi () and Yasutaka Shimizu ()
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Mitsuki Kobayashi: Waseda University
Yasutaka Shimizu: Waseda University

Statistical Inference for Stochastic Processes, 2023, vol. 26, issue 2, No 5, 411 pages

Abstract: Abstract We consider parameter estimation of stochastic differential equations driven by a Wiener process and a compound Poisson process as small noises. The goal is to give a threshold-type quasi-likelihood estimator and show its consistency and asymptotic normality under new asymptotics. One of the novelties of the paper is that we give a new localization argument, which enables us to avoid truncation in the contrast function that has been used in earlier works and to deal with a wider class of jumps in threshold estimation than ever before.

Keywords: Small noise asymptotics; Asymptotic distribution; Discrete observations; Primary 62M20; Secondary: 62F12; 60J74 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s11203-023-09286-y

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