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2012 Conditioned martingales
Nicolas Perkowski, Johannes Ruf
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Electron. Commun. Probab. 17: 1-12 (2012). DOI: 10.1214/ECP.v17-1955

Abstract

It is well known that upward conditioned Brownian motion is a three-dimensional Bessel process, and that a downward conditioned Bessel process is a Brownian motion. We give a simple proof for this result, which generalizes to any continuous local martingale and clarifies the role of finite versus infinite time in this setting. As a consequence, we can describe the law of regular diffusions that are conditioned upward or downward.

Citation

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Nicolas Perkowski. Johannes Ruf. "Conditioned martingales." Electron. Commun. Probab. 17 1 - 12, 2012. https://doi.org/10.1214/ECP.v17-1955

Information

Accepted: 9 October 2012; Published: 2012
First available in Project Euclid: 7 June 2016

zbMATH: 1266.60082
MathSciNet: MR2988394
Digital Object Identifier: 10.1214/ECP.v17-1955

Subjects:
Primary: 60G44
Secondary: 60H99, 60J60

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