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STATISTICAL CAUSALITY AND MARTINGALE REPRESENTATION PROPERTY WITH APPLICATION TO STOCHASTIC DIFFERENTIAL EQUATIONS

Published online by Cambridge University Press:  20 May 2014

LJILJANA PETROVIĆ
Affiliation:
Department of Mathematics and Statistics, Faculty of Economics, University of Belgrade, Kamenička 6, 11000 Beograd, Serbia email [email protected]
DRAGANA VALJAREVIĆ*
Affiliation:
Department of Mathematics, Faculty of Science, University of Kosovska Mitrovica, Lole Ribara 29, 38220 Kosovska Mitrovica, Serbia email [email protected]
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Abstract

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The paper considers a statistical concept of causality in continuous time between filtered probability spaces, based on Granger’s definition of causality. This causality concept is connected with the preservation of the martingale representation property when the filtration is getting smaller. We also give conditions, in terms of causality, for every martingale to be a continuous semimartingale, and we consider the equivalence between the concept of causality and the preservation of the martingale representation property under change of measure. In addition, we apply these results to weak solutions of stochastic differential equations. The results can be applied to the economics of securities trading.

Type
Research Article
Copyright
Copyright © 2014 Australian Mathematical Publishing Association Inc. 

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