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

Part of: Stochastic analysis Stochastic processes

Published online by Cambridge University Press:  20 May 2014

LJILJANA PETROVIĆ  and
DRAGANA VALJAREVIĆ
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]
*
✉[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.

Keywords

filtrationscausalityrepresentation propertysemimartingalestochastic differential equations

MSC classification

Secondary: 60G44: Martingales with continuous parameter 60H10: Stochastic ordinary differential equations
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 90 , Issue 2 , October 2014 , pp. 327 - 338
Copyright
Copyright © 2014 Australian Mathematical Publishing Association Inc. 

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