
Digital Library of the
European Council for Modelling and Simulation 
Title: 
Generation Of Probability Measures With The Given Specification Of The
Smallest Bans 
Authors: 
Alexander A. Grusho, Nick A. Grusho, Elena E. Timonina 
Published in: 
(2014).ECMS 2014 Proceedings edited
by: Flaminio Squazzoni,
Fabio Baronio, Claudia Archetti,
Marco Castellani European Council for
Modeling and Simulation. doi:10.7148/2014 ISBN:
9780956494481 28^{th}
European Conference on Modelling and Simulation, Brescia,
Italy, May 27^{th} – 30^{th},
2014 
Citation
format: 
Alexander
A. Grusho, Nick A. Grusho,
Elena E. Timonina (2014). Generation Of Probability Measures With The Given Specification Of The
Smallest Bans, ECMS 2014 Proceedings edited by: Flaminio
Squazzoni, Fabio Baronio,
Claudia Archetti, Marco Castellani European
Council for Modeling and Simulation. doi:10.7148/20140565 
DOI: 
http://dx.doi.org/10.7148/20140565 
Abstract: 
A ban means a sequence
which has zero probability in a finite space. Generation of
probability models is carried out, as a rule, from simpler models by
introduction of additional restrictions. However fulfilment
of required properties for stochastic processes requires the proof in case of
introduction of additional restrictions. In particular, the proof is required
that restrictions on admissibility of trajectories don’t destroy the property
of being a random process that is to satisfy to the Kolmogorov’s
theorem. The paper deals with conditions under
which introduction of restrictions on trajectories of random sequences according
to the given specification of the smallest bans again generates random
process. When the probability measure Q is generated by restrictions defined
by bans we consider testing of sequence of hypotheses H_{0, n :} Q_{n} against H_{1, n }: P_{n}, where Q possesses the specification of the
smallest bans, P is a uniform measure and Q_{n},
P_{n} are projections of measures Q and P.
The existence of consistency of sequence test defined by bans is
investigated. 
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