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2012 Filtered Azéma martingales
Umut Çetin
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Electron. Commun. Probab. 17: 1-13 (2012). DOI: 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. <br />


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Umut Çetin. "Filtered Azéma martingales." Electron. Commun. Probab. 17 1 - 13, 2012.


Accepted: 18 December 2012; Published: 2012
First available in Project Euclid: 7 June 2016

zbMATH: 1317.60049
MathSciNet: MR3005735
Digital Object Identifier: 10.1214/ECP.v17-2310

Primary: 60G35
Secondary: 60H10 , 60J55

Keywords: Azéma's martingale , excursions of Brownian motion , Local times , optional projection , skew Brownian motion

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