Nonparametric estimation of trend function for stochastic differential equations driven by a bifractional Brownian motion

Abstract

The 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 dXt=S(Xt)dt+εdBtH,K, X0=x0, 0≤t≤T,{\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,}}

Keywords

• bifractional brownian motion
• trend function
• kernel estimator
• stochastic differential equations
• nonparametric estimation
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