Stochastic comparisons of Itô processes
type: Item
instance of: scholarly article
title: Stochastic comparisons of Itô processes
zbMATH Open document ID: 0766.60066
DOI: 10.1016/0304-4149(93)90056-A
author: Bruno Bassan
author: Erhan Çinlar
author: Marco Scarsini
published in: Stochastic Processes and their Applications
publication date: 1993-05-16T00:00:00Z
review text: Stochastic comparisons are results in terms of the stochastic ordering \(\leq_{st}\), where, for random variables \(X_ 1\) and \(X_ 2\) taking values in a partially ordered measurable space, \(X_ 1\leq_{st}X_ 2\) if \(Eg(X_ 1)\leq Eg(X_ 2)\) for every increasing positive measurable function \(g\) on that space. Here the authors consider general Itô processes (i.e. solutions of stochastic differential equations of jump type). The laws of such processes are given essentially by three deterministic functions governing the drift, diffusion and jumps. This representation is particularly useful for stochastic comparisons, ``because it loads all the randomness onto the standard processes (Brownian and Poisson)''. Here stochastic comparisons for Itô processes are provided in terms of these deterministic functions. Results on semi- martingale Hunt processes are also supplied, and the detrimental effect of time changes on such comparisons is displayed.
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 60G99
Mathematics Subject Classification ID: 60J35
zbMATH DE Number: 167142
zbMATH Keywords: local characteristics
zbMATH Keywords: random time changes
zbMATH Keywords: stochastic comparisons
zbMATH Keywords: Itô processes
zbMATH Keywords: semi-martingale Hunt processes
reviewed by: Andrew Dale
MaRDI profile type: Publication
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full work available at URL: 0304-4149(93)90056-a
OpenAlex ID: W1991874872
description: scientific article; zbMATH DE number 167142