Drift estimation for rough processes under small noise asymptotic: trajectory fitting method

2025/03/05 by Gloter, Arnaud, Yoshida, Nakahiro · 1 citation
#FOS: Mathematics #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.2503.03347

Abstract

We consider a process X^ε solution of a stochastic Volterra equation with an unknown parameter θ^⋆ in the drift function. The Volterra kernel is singular and given by K(u)=c u^α-1/2 \mathbb1_u>0 with α∈ (0,1/2). It is assumed that the diffusion coefficient is proportional to ε → 0. From an observation of the path (X^ε_s)_s∈[0,T], we construct a Trajectory Fitting Estimator, which is shown to be consistent and asymptotically normal. We also specify identifiability conditions insuring the L^p convergence of the estimator.

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• Drift estimation for rough processes under small noise asymptotic : QMLE approach

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