Quadratic variation of martingales in Riesz spaces

被引：13

作者：

Grobler, Jacobus J. ^{[1
]}

Labuschagne, Coenraad C. A. ^{[2
,3
]}

Marraffa, Valeria ^{[4
]}

机构：

[1] North West Univ, Sch Comp Stat & Math Sci, Mmabatho, South Africa

[2] Univ Witwatersrand, Sch Computat & Appl Math, ZA-2050 Po Wits, South Africa

[3] Univ Johannesburg, Dept Finance & Investment Management, ZA-2006 Auckland Pk, South Africa

[4] Univ Palermo, Dipartimento Matemat & Informat, I-90123 Palermo, Italy

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2014年 / 410卷 / 01期

基金：

新加坡国家研究基金会;

关键词：

Austin's theorem; Martingale; Measure-free stochastic processes; Quadratic variation; Riesz space; Vector lattice; CONVERGENT MARTINGALES; PROPERTY;

D O I：

10.1016/j.jmaa.2013.08.037

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We derive quadratic variation inequalities for discrete-time martingales, sub- and super-martingales in the measure-free setting of Riesz spaces. Our main result is a Riesz space analogue of Austin's sample function theorem, on convergence of the quadratic variation processes of martingales. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：418 / 426

页数：9

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