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STATISTICAL INFERENCE FOR JUMP-FREE STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY FRACTIONAL BROWNIAN MOTION USING THE METHOD OF MOMENTS
Keywords:
stochastic differential equations (SDEs), fractional Brownian motion (fBm), statistical inference, drift parameter, diffusion parameter, jump-free models, fractional Langevin model, fractional Black-Scholes model, fractional Ornstein-Uhlenbeck model, fractional Lévy process, method of moments, asymptotic properties, consistency, asymptotic normality, long-memory processes, time series analysisDOI:
https://doi.org/10.17654/0972361725026Abstract
This work addresses statistical inference for jump-free stochastic differential equations (SDEs) driven by fractional Brownian motion (fBm), a significant area of research in probability theory with applications across finance, physics, and natural sciences. Parameter estimation in SDEs, especially for drift and diffusion parameters, presents considerable challenges due to the complexity of these models. We investigate various statistical inference approaches for fBm-based models, focusing on the method of moments for parameter estimation. We begin by constructing estimators for both drift and diffusion parameters using this approach, applying it to different types of jump-free SDEs. Our study concludes with an analysis of the asymptotic properties of the estimators, including consistency and asymptotic normality. This work contributes to a deeper understanding of the unique challenges and potentials of these sophisticated models in capturing long-memory effects and dependencies in data.
Received: November 1, 2024
Revised: December 12, 2024
Accepted: January 4, 2025
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