Translator Disclaimer
December 2015 Local martingales with two reflecting barriers
Mats Pihlsgård
Author Affiliations +
J. Appl. Probab. 52(4): 1062-1075 (December 2015). DOI: 10.1239/jap/1450802753

Abstract

We give an account of the characteristics that result from reflecting a drifting local martingale (i.e. the sum of a local martingale and a multiple of its quadratic variation process) in 0 and b > 0. We present conditions which guarantee the existence of finite moments of what is required to keep the reflected process within its boundaries. Also, we derive an associated law of large numbers and a central limit theorem which apply when the input is continuous. Similar results for integrals of the paths of the reflected process are also presented. These results are in close agreement to what has previously been shown for Brownian motion.

Citation

Download Citation

Mats Pihlsgård. "Local martingales with two reflecting barriers." J. Appl. Probab. 52 (4) 1062 - 1075, December 2015. https://doi.org/10.1239/jap/1450802753

Information

Published: December 2015
First available in Project Euclid: 22 December 2015

zbMATH: 1334.60069
MathSciNet: MR3439172
Digital Object Identifier: 10.1239/jap/1450802753

Subjects:
Primary: 60G44, 60G51, 60H05
Secondary: 60G17

Rights: Copyright © 2015 Applied Probability Trust

JOURNAL ARTICLE
14 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.52 • No. 4 • December 2015
Back to Top