Large deviations for martingales via Cramér's method

Ion Grama and Erich Haeusler

Stochastic Processes and their Applications, 2000, vol. 85, issue 2, 279-293

Abstract: We develop a new approach for proving large deviation results for martingales based on a change of probability measure. It extends to the case of martingales the conjugate distribution technique due to Cramér. To demonstrate our approach, we derive formulae for probabilities of large deviations for martingales with bounded jumps and bounded norming factor. Surprisingly enough, our result shows that the relative error in the normal range is of the same order as in the case of sums of independent random variables. It also allows to extend the range beyond the normal one.

Keywords: Martingales; Large; deviations; Rate; of; convergence (search for similar items in EconPapers)
Date: 2000
References: View complete reference list from CitEc
Citations: View citations in EconPapers (8)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304-4149(99)00079-4
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:85:y:2000:i:2:p:279-293

Ordering information: This journal article can be ordered from
http://http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Stochastic Processes and their Applications is currently edited by T. Mikosch

More articles in Stochastic Processes and their Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().