Statistical causality and adapted distribution

In the paper D. Hoover, J. Keisler : Adapted probability distributions, Trans. Amer. Math. Soc. 286 (1984), 159–201 the notion of adapted distribution of two stochastic processes was introduced, which in a way represents the notion of equivalence of those processes. This very important property is h...

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Veröffentlicht in:Czechoslovak mathematical journal 2011-09, Vol.61 (3), p.827-843
Hauptverfasser: Petrović, Ljiljana, Dimitrijević, Sladjana
Format: Artikel
Sprache:eng
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Zusammenfassung:In the paper D. Hoover, J. Keisler : Adapted probability distributions, Trans. Amer. Math. Soc. 286 (1984), 159–201 the notion of adapted distribution of two stochastic processes was introduced, which in a way represents the notion of equivalence of those processes. This very important property is hard to prove directly, so we continue the work of Keisler and Hoover in finding sufficient conditions for two stochastic processes to have the same adapted distribution. For this purpose we use the concept of causality between stochastic processes, which is based on Granger’s definition of causality. Also, we provide applications of our results to solutions of some stochastic differential equations.
ISSN:0011-4642
1572-9141
DOI:10.1007/s10587-011-0030-1