On a calculable Skorokhod’s integral based projection estimator of the drift function in fractional SDE

Nicolas Marie ()
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Nicolas Marie: Université Paris Nanterre

Statistical Inference for Stochastic Processes, 2024, vol. 27, issue 2, No 5, 405 pages

Abstract: Abstract This paper deals with a Skorokhod’s integral based projection type estimator $${\widehat{b}}_m$$ b ^ m of the drift function $$b_0$$ b 0 computed from $$N\in \mathbb N^*$$ N ∈ N ∗ independent copies $$X^1,\dots ,X^N$$ X 1 , ⋯ , X N of the solution X of $$dX_t = b_0(X_t)dt +\sigma dB_t$$ d X t = b 0 ( X t ) d t + σ d B t , where B is a fractional Brownian motion of Hurst index $$H\in (1/2,1)$$ H ∈ ( 1 / 2 , 1 ) . Skorokhod’s integral based estimators cannot be calculated directly from $$X^1,\dots ,X^N$$ X 1 , ⋯ , X N , but in this paper an $$\mathbb L^2$$ L 2 -error bound is established on a calculable approximation of $${\widehat{b}}_m$$ b ^ m .

Keywords: Fractional Brownian motion; Projection estimator; Malliavin calculus; Stochastic differential equations (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s11203-024-09306-5

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