Stopped two-dimensional perturbed random walks and Lévy processes
type: Item
instance of: scholarly article
title: Stopped two-dimensional perturbed random walks and Lévy processes
zbMATH Open document ID: 0890.60021
DOI: 10.1016/S0167-7152(97)00028-X
published in: Statistics \& Probability Letters
publication date: 1998-06-23T00:00:00Z
review text: The author presents some limit theorems for stopped and perturbed two-dimensional random walks and Lévy processes. In particular, a strong limit theorem for the process(es) and a central limit theorem for the overshoots are established. The results are subsequently specialized to processes of the type \(Z^{(i)}_n= ng^{(i)}(n^{-1}(X^{(i)}_1+\cdots+ X^{(i)}_n))\), \(i= 1,2\), with i.i.d. sequences \(\{X^{(i)}_n\}_{n\in \mathbb{N}}\) of integrable random variables and certain real functions \(g_1\), \(g_2\). An application to repeated significance tests in two-parameter exponential families is given. The paper contains only rough sketches of some proofs. For most of the material the reader is being referred to (suitably adapted versions of the) proofs in various previously published papers by the author and co-authors.
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60J99
Mathematics Subject Classification ID: 60G50
Mathematics Subject Classification ID: 60K05
Mathematics Subject Classification ID: 62L10
zbMATH DE Number: 1092021
zbMATH Keywords: perturbed Lévy process
zbMATH Keywords: stopped process
zbMATH Keywords: central limit theorem
zbMATH Keywords: first passage time
author: Allan Gut
reviewed by: R. L. Schilling
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1092021