Some Remarks on Stationary Possibilistic Processes
نویسندگان
چکیده
We investigate the following extendability problem for systems, for which the available information is given by a monotone set mapping M on the field CT of measurable cylinders of a product ample space (XT ,RT ): given that M is invariant under a RT −RT measurable transformation H of XT , i.e. M(H−1(B)) = M(B) for all B ∈ CT , is it possible to find H-invariant monotone extensions of M to the powerclass of XT ? We first show that the outer and inner measures of M always have the desired invariance property. If the system that we are dealing with is possibilistic, a number of sufficient conditions are derived to ensure the H-invariance of the greatest possibilistic extension ΠM of M. Consequently stationary possibilistic processes can be represented by a shift-invariant possibility measure on their basic space. As an illustration for our results, we show that possibilistic Markov processes with stationary transition possibilities and stationary initial possibilities are stationary processes.
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تاریخ انتشار 1998