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STATISTICAL CAUSALITY AND STABLE SUBSPACES OF $H^P$

Part of: Stochastic processes

Published online by Cambridge University Press:  01 August 2012

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: petrovl@ekof.bg.ac.rs)
DRAGANA VALJAREVIĆ*
Affiliation:
Department of Mathematics, Faculty of Science, University of Priština-Kosovska Mitrovica, Lole Ribara 29, 38220 Kosovska Mitrovica, Serbia (email: dragana_stan@yahoo.com)
*
✉For correspondence; e-mail: dragana˙stan@yahoo.com
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Abstract

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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 $P(A \mid {\mathcal {G}}_t)$. 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.

Keywords

filtrationscausalitystable subspacesextremal measuresstochastic differential equations

MSC classification

Secondary: 60G44: Martingales with continuous parameter
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 88 , Issue 1 , August 2013 , pp. 17 - 25
Copyright
Copyright © 2012 Australian Mathematical Publishing Association Inc. 

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