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Causal predictability and weak solutions of the stochastic differential equations with driving semimartingales

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  • Merkle, Ana

Abstract

We consider causal relationships between σ-fields (filtrations) in continuous time and define the concept of dependence between filtrations, named causal predictability, which is based on the Granger’s definition of causality. The concept of causality is analyzed using the tool of conditional independence. Then, we provide some properties of the given predictability concept.

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  • Merkle, Ana, 2023. "Causal predictability and weak solutions of the stochastic differential equations with driving semimartingales," Statistics & Probability Letters, Elsevier, vol. 197(C).
    • Handle: RePEc:eee:stapro:v:197:y:2023:i:c:s0167715223000408
    DOI: 10.1016/j.spl.2023.109816
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    1. Florens, J.P. & Mouchart, M., 1982. "A note on noncausality," LIDAM Reprints CORE 479, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Valjarević, Dragana & Merkle, Ana, 2021. "Statistical causality and measurable separability of σ-algebras," Statistics & Probability Letters, Elsevier, vol. 177(C).
    3. Florens, J P & Mouchart, M, 1982. "A Note on Noncausality," Econometrica, Econometric Society, vol. 50(3), pages 583-591, May.
    4. MOUCHART, Michel & ROLIN, Jean-Marie, 1985. "A note on conditional independence with statistical applications," LIDAM Reprints CORE 630, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Florens, Jean-Pierre & Fougere, Denis, 1996. "Noncausality in Continuous Time," Econometrica, Econometric Society, vol. 64(5), pages 1195-1212, September.
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