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A class of remarkable submartingales


Nikeghbali, A (2006). A class of remarkable submartingales. Stochastic Processes and their Applications, 116(6):917-938.

Abstract

In this paper, we consider the special class of positive local submartingales (Xt) of the form Xt=Nt+At, where the measure View the MathML source is carried by the set {t:Xt=0}. We show that many examples of stochastic processes studied in the literature are in this class and propose a unified approach based on martingale techniques for studying them. In particular, we establish some martingale characterizations for these processes and compute explicitly some distributions involving the pair (Xt,At). We also associate with X a solution to the Skorokhod’s stopping problem for probability measures on the positive half-line.

Abstract

In this paper, we consider the special class of positive local submartingales (Xt) of the form Xt=Nt+At, where the measure View the MathML source is carried by the set {t:Xt=0}. We show that many examples of stochastic processes studied in the literature are in this class and propose a unified approach based on martingale techniques for studying them. In particular, we establish some martingale characterizations for these processes and compute explicitly some distributions involving the pair (Xt,At). We also associate with X a solution to the Skorokhod’s stopping problem for probability measures on the positive half-line.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Scopus Subject Areas:Physical Sciences > Statistics and Probability
Physical Sciences > Modeling and Simulation
Physical Sciences > Applied Mathematics
Language:English
Date:June 2006
Deposited On:04 Nov 2009 15:06
Last Modified:21 Jan 2022 14:23
Publisher:Elsevier
ISSN:0304-4149
OA Status:Hybrid
Publisher DOI:https://doi.org/10.1016/j.spa.2005.12.003
Related URLs:http://www.ams.org/mathscinet-getitem?mr=2254665
http://arxiv.org/abs/math/0505515
  • Content: Accepted Version
  • Description: Accepted manuscript, Version 2
  • Content: Accepted Version
  • Description: Accepted manuscript, Version 1