Nonparametric estimation of trend function for stochastic differential equations driven by a bifractional Brownian motion
The main objective of this paper is to investigate the problem of estimating the trend function S = S(x ) for process satisfying stochastic differential equations of the type where { } is a bifractional Brownian motion with known parameters H (0, 1), K (0, 1] and HK (1/2, 1). We estimate the unknown...
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Veröffentlicht in: | Acta universitatis sapientiae. Mathematica 2020-07, Vol.12 (1), p.128-145 |
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Hauptverfasser: | , , |
Format: | Artikel |
Sprache: | eng |
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Zusammenfassung: | The main objective of this paper is to investigate the problem of estimating the trend function S
= S(x
) for process satisfying stochastic differential equations of the type
where {
} is a bifractional Brownian motion with known parameters H
(0, 1), K
(0, 1] and HK
(1/2, 1). We estimate the unknown function S(x
) by a kernel estimator ̂S
and obtain the asymptotic properties as ε → 0. Finally, a numerical example is provided. |
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ISSN: | 2066-7752 2066-7752 |
DOI: | 10.2478/ausm-2020-0008 |