Nonparametric estimation of linear multiplier for processes driven by a Hermite process

B. L. S. Prakasa Rao
Theory of Stochastic Processes
Vol.30 (46), no.1, 2026, pp.48-60

We study the problem of nonparametric estimation of the linear multiplier function θ(t) for processes satisfying stochastic differential equations of the type

dX_t = θ(t) dX_t dt + ε dZ_t^q,H, X₀ = x₀, 0 ≤ t ≤ T

where {Z_t^q,H, t ≥ 0} is a Hermite process with known order q and known self-similarity parameter H ∈ (½,1). We study the asymptotic behaviour of the estimator of the unknown function θ(t) as ε → 0.

DOI: https://doi.org/10.3842/tsp-6713112929-29
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