BAYESIAN ESTIMATION OF DRIFT FRACTIONAL BROWNIAN MOTION AT DISCRETE OBSERVATIONS

Leixin Xia, Baojiang Chen and Dejian Lai
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Leixin Xia: Department of Biostatistics and Data Science, The University of Texas Health Science Center at Houston, School of Public Health, Houston, TX 77030, USA
Baojiang Chen: Department of Biostatistics and Data Science, The University of Texas Health Science Center at Houston, School of Public Health, Houston, TX 77030, USA
Dejian Lai: Department of Biostatistics and Data Science, The University of Texas Health Science Center at Houston, School of Public Health, Houston, TX 77030, USA

FRACTALS (fractals), 2025, vol. 33, issue 09, 1-7

Abstract: The purpose of this paper is to estimate the three unknown parameters H,𠜃 and σ in drift fractional Brownian motion using the Bayesian method. The maximum a posteriori (MAP) estimator is chosen as the point estimator. We derived easy to use closed form for estimating 𠜃 and σ. Our simulation results demonstrated that our method works well with a small sample size, missing, and irregular observations.

Keywords: Bayesian Method; Fractional Brownian Motion; MAP Estimator; Simulation Studies (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0218348X25500719

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