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
Issue Date: 2021-03-01
Rights link:
Appears in Collections:Lehrstuhl IV Stochastik und Analysis

Files in This Item:
File Description SizeFormat 
Schulmann2021_Article_EstimationOfStoppingTimesForSt.pdf621.16 kBAdobe PDFView/Open

This item is protected by original copyright

This item is licensed under a Creative Commons License Creative Commons