Statistical causality, martingale problems and local uniqueness. Issue 2 (17th February 2018)

• Record Type: Journal Article
• Authors: Petrović, Ljiljana; Valjarević, Dragana
• Is Part Of: Stochastics. Volume 90:Issue 2(2018)
• Page Start: 200
• Page End: 213
• Publication Date: 2018-02-17
• Subjects: Causality -- martingale problem -- stopped martingale problem -- local martingale problem -- strict stopping time -- local uniqueness; Stochastic processes -- Periodicals; Probabilities -- Periodicals; 519.2
• DOI: 10.1080/17442508.2017.1318137
• Languages: English
• ISSNs: 1744-2508

Abstract

Abstract: The paper considers a statistical concept of causality in continuous time in the filtered probability spaces which is based on the Granger's definition of causality. The given causality concept is then applied to the solution of the martingale problem (associated with the stochastic differential equation driven with semimartingales). More precisely, we show that the given causality concept is closely connected to the concept of extremality of measures for the solutions of the martingale problem, for the stopped martingale problem and for the local martingale problem. We also show the equivalence between some models of causality and local uniqueness (for the solutions of the martingale problem).