Use of the important sampling in the Monte Carlo method (Q2729353)

The authors study the problem of calculating the normalized density constant in the case of a given sampling. This problem appears in the study of limit distributions of the so-called Monte Carlo Markov chains and in the case when an approximation of the density is constructed by using the stochastic values. To solve the above-mentioned problem, the authors expose a numerical method which presents an analog of the sampling algorithm with respect to the importance characteristic where the important sampling values are used. The authors show that if the integral is calculated by the Monte Carlo method and the important sampling is not given in advance, then it is more appropriately to use close-to-important sampling values rather than important sampling. In this case, the authors demonstrate a new algorithm called the two-sided geometric method and indicate that this algorithm makes it possible to reduce the cost of calculations.