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
Hauptverfasser: Keddi, Abdelmalik, Madani, Fethi, Bouchentouf, Amina Angelika
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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.
ISSN:2066-7752
2066-7752
DOI:10.2478/ausm-2020-0008