Statistical causality and adapted distribution |
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Authors: | Ljiljana Petrovi? Sladjana Dimitrijevi? |
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Institution: | 1.Beograd,Serbia;2.Kragujevac,Serbia;3.Faculty of Economics,University of Belgrade,Belgrade,Serbia;4.Faculty of Science,University of Kragujevac,Kragujevac,Serbia |
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Abstract: | 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. |
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