Modern Stochastics: Theory and Applications

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Stanislav Lohvinenko Kostiantyn Ralchenko

Pub. online: 23 Sep 2019 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 6, Issue 3 (2019), pp. 377–395

Abstract

We investigate the fractional Vasicek model described by the stochastic differential equation

$d{X_{t}}=(\alpha -\beta {X_{t}})\hspace{0.1667em}dt+\gamma \hspace{0.1667em}d{B_{t}^{H}}$ ,

${X_{0}}={x_{0}}$ , driven by the fractional Brownian motion

${B^{H}}$ with the known Hurst parameter

$H\in (1/2,1)$ . We study the maximum likelihood estimators for unknown parameters α and β in the non-ergodic case (when

$\beta <0$ ) for arbitrary

${x_{0}}\in \mathbb{R}$ , generalizing the result of Tanaka, Xiao and Yu (2019) for particular

${x_{0}}=\alpha /\beta$ , derive their asymptotic distributions and prove their asymptotic independence.

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