Estimation of stopping times for stopped self-similar random processes

Viktor Schulmann ()
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Viktor Schulmann: Technische Universität Dortmund

Statistical Inference for Stochastic Processes, 2021, vol. 24, issue 2, No 8, 477-498

Abstract: Abstract Let $$X=(X_t)_{t\ge 0}$$ X = ( X t ) t ≥ 0 be a known process and T an unknown random time independent of X. Our goal is to derive the distribution of T based on an iid sample of $$X_T$$ X T . Belomestny and Schoenmakers (Stoch Process Appl 126(7):2092–2122, 2015) propose a solution based the Mellin transform in case where X is a Brownian motion. Applying their technique we construct a non-parametric estimator for the density of T for a self-similar one-dimensional process X. We calculate the minimax convergence rate of our estimator in some examples with a particular focus on Bessel processes where we also show asymptotic normality.

Keywords: Estimation of stopping times; Multiplicative deconvolution; Mellin transform; Self-similar process; Bessel process; 62G07; 62G20; 60G18; 60G40 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s11203-020-09234-0

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