Maximal inequalities for CIR processes
type: Item
instance of: scholarly article
title: Maximal inequalities for CIR processes
zbMATH Open document ID: 1056.60080
author: Litan Yan
author: Yingchun Li
published in: Letters in Mathematical Physics
publication date: 2004-08-16T00:00:00Z
review text: Let \(X\) be a Cox-Ingersoll-Ross process solving the stochastic differential equation \[ dX_t=(a+bX_t)dt+c\sqrt{| X_t| }dB_t \] with \(X_0=0\), where \(a, c > 0\), \(b \in {\mathbb R}\) and \(B\) is a standard Brownian motion started at zero. Some inequalities between the integral functional \(J_{\varphi}(t)=\int_0^t\varphi(X_s)ds\), \(t \geq 0\), and the maximum process \(\sup_{0 \leq s \leq t} X_t\), \(t \geq 0\), where \(x \mapsto \varphi(x)\) is a nonnegative continuous function with some suitable conditions, are derived.
Mathematics Subject Classification ID: 60J60
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 60E15
Mathematics Subject Classification ID: 60G40
zbMATH DE Number: 2091492
zbMATH Keywords: Bessel processes and domination principle
zbMATH Keywords: Cox-Ingersoll-Ross process
zbMATH Keywords: diffusion process
zbMATH Keywords: Itô's formula, maximal inequalities
reviewed by: Pavel Gapeev
MaRDI profile type: Publication
full work available at URL: b:math.0000032705.81302.2d
OpenAlex ID: W2012608722
DOI: 10.1023/B:MATH.0000032705.81302.2D
description: scientific article; zbMATH DE number 2091492