Filtered Azéma martingales

Umut Çetin

doi:10.1214/ECP.v17-2310

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Home > Journals > Electron. Commun. Probab. > Volume 17 > Article

2012 Filtered Azéma martingales

Umut Çetin

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Umut Çetin¹
¹London School of Economics and Political Science

Electron. Commun. Probab. 17: 1-13 (2012). DOI: 10.1214/ECP.v17-2310

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Abstract

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 />