Non‐parametric Kernel Estimation of the Coefficient of a Diffusion

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Penalized nonparametric mean square estimation of the coefficients of diffusion processes (2007, background): “Then the estimator σ̂2 m of σ2 defined by (20) is such that (24) E(‖σ̂(2) m − σ(2) A‖(2)n) ≤ 7π1‖σ(2) m − σ(2) A‖(2) +K E(σ(4)(X0))Dm n +K ′∆2 + K” n , where σ2 A = σ (2)1I[0,1], and K, K ′, K” are some positive constants.”
Comment: A Selective Overview of Nonparametric Methods in Financial Econometrics (2005, background): “Other estimators of the diffusion coefficient were proposed by Soulier [23] and Jacod [ 15 ].”