Statistical causality and stable subspaces of \(H^p\)

Authors

  • Lj. Petrovic Faculty of Economics, University of Belgrade
  • D. Valjarevic Faculty of Science,

Keywords:

Filtrations, causality, stable subspaces, extremal measures, stochastic differential equations

Abstract

The paper considers a statistical concept of causality in continuous time between filtered probability spaces which is based on Granger's definitions of causality. Then, we consider some stable subspaces of $H^p$ which contains the 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 the stochastic differential equations. 10.1017/S0004972712000482

Author Biographies

Lj. Petrovic, Faculty of Economics, University of Belgrade

Department of Mathematics and Statistics

D. Valjarevic, Faculty of Science,

Department of Mathematics

Published

2013-07-23

Issue

Vol. 88 No. 1 (2013)

Section

Articles
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