Stochastic model for determination of arbitrariness and completeness of information system

Abstract

When evaluating information system reliability indicators, the necessary initial data for a priori probability calculations are often missing, and statistical evaluation is complicated by a large amount of tests, which can only be used to determine the estimates of the moments of the determining random variables of the process of functioning of the information system or its constituent parts (mathematical expectation and variance of failure time processing, recovery time, backup time, etc.). However, in this situation, it is necessary to justify some characteristics of the information system, for example, time reserve, guaranteed exact limits of the probability of fault-free operation of the system and availability coefficient. In this case, «justification» means the construction of precise upper and lower limits of the change of functionals, which characterize the efficiency of the functioning of the information system, in the conditions of incomplete a priori information about the distribution functions of the determining random variables. In this paper, an N-periodic set of information states with one risky and one risk-free process is considered, the arbitrariness and completeness of this set is investigated, and the entropy for the Radon-Nikodym derivative of the corresponding equivalent martingale measures is found. Conditions for the signal loss distribution function were also found, under which the set of signal states is arbitragefree and complete. It is shown that the use of the proposed signal change function made it possible to effectively investigate a set of information states for impartiality and completeness. The application of the obtained results to the determination of the fair price for the аsian arithmetic option with the initially specified payment function is considered.