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Filtered Azéma martingales

Cetin, Umut (2012) Filtered Azéma martingales. Electronic Communications in Probability, 17. ISSN 1083-589X

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Identification Number: 10.1214/ECP.v17-2310


We study the optional projection of a standard Brownian motion on the natural filtration of certain kinds of observation processes. The observation process, Y, is defined as a solution of a stochastic differential equation such that it reveals some (possibly noisy) information about the signs of the Brownian motion when Y hits 0. As such, the associated optional projections are related to Azéma's martingales which are obtained by projecting the Brownian motion onto the filtration generated by observing its signs.

Item Type: Article
Official URL:
Additional Information: © 2012 The Author
Divisions: LSE
Subjects: H Social Sciences > HA Statistics
Date Deposited: 10 Jan 2013 14:08
Last Modified: 20 Apr 2021 00:55

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