Reflecting or sticky Markov processes with Lévy generators as the limit of storage processes
type: Item
instance of: scholarly article
title: Reflecting or sticky Markov processes with Lévy generators as the limit of storage processes
zbMATH Open document ID: 0811.60067
DOI: 10.1016/0304-4149(94)90105-8
author: Keigo Yamada
published in: Stochastic Processes and their Applications
publication date: 1995-04-19T00:00:00Z
review text: The author considers the approximation to reflecting or sticky diffusions or more generally Markov processes with Lévy generators having nondegenerate diffusion coefficients of a sequence of storage processes of the following type, \[ X(t)= X(0)- \int_ 0^ t r(X(s)) ds+ \int_ 0^ t\;\int_{u>0} uN(ds, du)-\xi(t), \] where \(X(t)\) takes values in \([0,K]\) (possibly \(K=\infty\)), \(N(ds,dx)\) is an integer-valued random measure with compensator \(ds d\nu (u\mid X(s))\) and \(\xi(t)\) is increasing: \[ \xi(0)=0, \qquad \xi(t)= \int_ 0^ t 1_{\{K\}} (X(s)) d\xi(s), \] under suitable conditions imposed on \(r\) and \(d\nu (u\mid x)\). The author claims the general limit theorems for semimartingles cannot be directly applied owing to the special conditions posed in his approach. Some examples satisfying these conditions are given, including \textit{J. M. Harrison} and \textit{A. J. Lemoine's} model [J. Appl. Probab. 18, 216-226 (1981; Zbl 0453.60072)].
Mathematics Subject Classification ID: 60J75
Mathematics Subject Classification ID: 60J60
zbMATH DE Number: 672065
zbMATH Keywords: storage process
zbMATH Keywords: sticky Markov process
zbMATH Keywords: state-dependent Lévy measure
zbMATH Keywords: integer-valued random measure
zbMATH Keywords: limit theorems for semimartingles
MaRDI profile type: Publication
full work available at URL: 0304-4149(94)90105-8
OpenAlex ID: W2048362551
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description: scientific article; zbMATH DE number 672065