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Local martingales with two reflecting barriers

Pihlsgård, Mats LU (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.
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author
organization
publishing date
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
2016-03-01 07:16:34
date last changed
2017-01-01 03:58:35
@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},
  keyword      = {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},
  volume       = {52},
  year         = {2015},
}