Authors: | Schulmann, Viktor |
Title: | Estimation of stopping times for stopped self-similar random processes |
Language (ISO): | en |
Abstract: | Let X=(Xt)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 XT. 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. |
Subject Headings: | Estimation of stopping times Multiplicative deconvolution Mellin transform Self-similar process Bessel process |
URI: | http://hdl.handle.net/2003/40240 http://dx.doi.org/10.17877/DE290R-22113 |
Issue Date: | 2021-03-01 |
Rights link: | https://creativecommons.org/licenses/by/4.0/ |
Appears in Collections: | Lehrstuhl IV Stochastik und Analysis |
Files in This Item:
File | Description | Size | Format | |
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Schulmann2021_Article_EstimationOfStoppingTimesForSt.pdf | 621.16 kB | Adobe PDF | View/Open |
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