On Probability Chains with Polynomial Growth
Author(s):
Natalia Vladislavovna Loginova
Senior Software Engineer
"Epam systems Montenegro" DOO Podgorica
Abstract:
The article is devoted to method of mathematical modeling of the resource allocation
process - the method of probabilistic chains. This model is a discrete dynamical system
defined on a simplex of probability vectors. Probabilistic chains with logistic and linear-logarithmic
growth have been studied in the most detail. In this paper, we consider chains with polynomial
growth. The polynomials of the system can be specified by different ways. We compare
arbitrary and optimized methods for choice of polynomials. The optimization is achieved
by taking into account the relationship between the influence of the share of the resource
in one territory on the share of the resource in another territory. As an example,
the data on trade in goods in % of GDP of Germany, France, Italy, Spain are considered.
The chains with logistic and linear-logarithmic growth are constructed as well.
The obtained results of modeling were analyzed by using the correlation coefficient,
which takes the greatest value for chains with polynomial growth constructed by the
optimized way.
Keywords
- extrapolation
- mathematical modeling
- polynomial growth
- probability chains
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