a1 Department of Mathematics and Statistics, Faculty of Economics, University of Belgrade, Kamenička 6, 11000 Beograd, Serbia (email: firstname.lastname@example.org)
a2 Department of Mathematics, Faculty of Science, University of Priština-Kosovska Mitrovica, Lole Ribara 29, 38220 Kosovska Mitrovica, Serbia (email: email@example.com)
In this paper we consider the statistical concept of causality in continuous time between filtered probability spaces, based on Granger’s definitions of causality. Then we consider some stable subspaces of H p which contain right continuous modifications of martingales P(A∣𝒢 t ). We give necessary and sufficient conditions, in terms of statistical causality, for these spaces to coincide with H p . These results can be applied to extremal measures and regular weak solutions of stochastic differential equations.
(Received May 17 2012)
(Accepted May 23 2012)
2010 Mathematics subject classification
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The work is supported by the Serbian Ministry of Science and Technology (Grants 044006 and 179005).