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Estimation of stopping times for stopped self-similar random processes

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  • Viktor Schulmann

    (Technische Universität Dortmund)

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.

Suggested Citation

  • Viktor Schulmann, 2021. "Estimation of stopping times for stopped self-similar random processes," Statistical Inference for Stochastic Processes, Springer, vol. 24(2), pages 477-498, July.
    • Handle: RePEc:spr:sistpr:v:24:y:2021:i:2:d:10.1007_s11203-020-09234-0
    DOI: 10.1007/s11203-020-09234-0
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    References listed on IDEAS

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    1. Belomestny, Denis & Schoenmakers, John, 2015. "Statistical Skorohod embedding problem: Optimality and asymptotic normality," Statistics & Probability Letters, Elsevier, vol. 104(C), pages 169-180.
    2. Belomestny, Denis & Schoenmakers, John, 2016. "Statistical inference for time-changed Lévy processes via Mellin transform approach," Stochastic Processes and their Applications, Elsevier, vol. 126(7), pages 2092-2122.
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