Local martingales with two reflecting barriers
(2015) In Journal of Applied Probability 52(4). p.1062-1075- 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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/8738936
- author
- Pihlsgård, Mats LU
- organization
- publishing date
- 2015
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Skorokhod problem, reflection, stochastic integration, Brownian motion, local martingale, semimartingale
- in
- Journal of Applied Probability
- volume
- 52
- issue
- 4
- pages
- 1062 - 1075
- publisher
- Applied Probability Trust
- external identifiers
-
- wos:000368467600011
- scopus:84952900336
- ISSN
- 1475-6072
- language
- English
- LU publication?
- yes
- id
- 51f573df-91d0-4935-8d06-e5978902b8df (old id 8738936)
- alternative location
- https://projecteuclid.org/euclid.jap/1450802753
- date added to LUP
- 2016-04-01 10:52:45
- date last changed
- 2022-04-28 02:18:56
@article{51f573df-91d0-4935-8d06-e5978902b8df,
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.}},
author = {{Pihlsgård, Mats}},
issn = {{1475-6072}},
keywords = {{Skorokhod problem; reflection; stochastic integration; Brownian motion; local martingale; semimartingale}},
language = {{eng}},
number = {{4}},
pages = {{1062--1075}},
publisher = {{Applied Probability Trust}},
series = {{Journal of Applied Probability}},
title = {{Local martingales with two reflecting barriers}},
url = {{https://projecteuclid.org/euclid.jap/1450802753}},
volume = {{52}},
year = {{2015}},
}