Optimal estimation of local time and occupation time measure for an α-stable Levy process

2022/10/14 by Chiara Amorino, Amorino, Chiara, Arturo Jaramillo +3
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2210.07672

openalex publication_date 2022/10/14 · openalex created_date 2022/10/19 · openalex updated_date 2026/07/28

Abstract

We present a novel theoretical result on estimation of local time and occupation time measure of an α-stable Lévy process with α in (1, 2). Our approach is based upon computing the conditional expectation of the desired quantities given high frequency data, which is an L²-optimal statistic by construction. We prove the corresponding stable central limit theorems and discuss a statistical application. In particular, this work extends the results of [Ivanovs and i Podolskij (2021)], which investigated the case of the Brownian motion.

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