Statistical causality and adapted distribution. (English) Zbl 1249.60063

Summary: D. N. Hoover and H. J. Keisler [Trans. Am. Math. Soc. 286, 159–201 (1984; Zbl 0548.60019)] introduced the notion of the adapted distribution of two stochastic processes, 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. We also provide applications of our results to solutions of some stochastic differential equations.


60G07 General theory of stochastic processes
03C98 Applications of model theory
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)


Zbl 0548.60019
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