Nonparametric estimation of trend function for stochastic differential equations driven by a bifractional Brownian motion
2020 ◽
Vol 12
(1)
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pp. 128-145
Keyword(s):
AbstractThe main objective of this paper is to investigate the problem of estimating the trend function St = S(xt) for process satisfying stochastic differential equations of the type {\rm{d}}{{\rm{X}}_{\rm{t}}} = {\rm{S}}\left( {{{\rm{X}}_{\rm{t}}}} \right){\rm{dt + }}\varepsilon {\rm{dB}}_{\rm{t}}^{{\rm{H,K}}},\,{{\rm{X}}_{\rm{0}}} = {{\rm{x}}_{\rm{0}}},\,0 \le {\rm{t}} \le {\rm{T,}}where {{\rm{B}}_{\rm{t}}^{{\rm{H,K}}},{\rm{t}} \ge {\rm{0}}} 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(xt) by a kernel estimator ̂St and obtain the asymptotic properties as ε → 0. Finally, a numerical example is provided.
2011 ◽
Vol 14
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pp. 101-109
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2020 ◽
Vol 28
(2)
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pp. 113-122
2019 ◽
Vol 37
(2)
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pp. 271-280
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2017 ◽
Vol 25
(4)
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2003 ◽
Vol 11
(3)
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2021 ◽
Vol 37
(7)
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pp. 1156-1170