On the first passage times for Markov processes with monotone convex transition kernels
type: Item
instance of: scholarly article
title: On the first passage times for Markov processes with monotone convex transition kernels
zbMATH Open document ID: 0833.60088
DOI: 10.1016/0304-4149(95)00020-8
author: Haijun Li
author: Moshe Shaked
published in: Stochastic Processes and their Applications
publication date: 1995-10-09T00:00:00Z
review text: For the Markov process \(Z_t\), \(t \geq 0\), with partially ordered Polish state space, the random time \[ T(x,y) = \inf \{t \geq 0 : Z_t > x \text{ or } Z_t - Z_{t-} > y\} \] is considered. It is shown that under certain conditions the time \(T\) possesses the NBU, IFRA or IFR properties. The main of the conditions is the monotonicity and convexity of the corresponding transition kernel. The obtained results are applied to the pure jump shock model.
Mathematics Subject Classification ID: 60K10
Mathematics Subject Classification ID: 60J25
Mathematics Subject Classification ID: 60J75
zbMATH DE Number: 803386
zbMATH Keywords: first passage time
zbMATH Keywords: stochastic monotonicity
zbMATH Keywords: jump process
zbMATH Keywords: pure jump shock model
reviewed by: Eugene Kozarovitsky
MaRDI profile type: Publication
full work available at URL: 0304-4149(95)00020-8
OpenAlex ID: W2011245400
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description: scientific article; zbMATH DE number 803386