Two curves characterizing a set of realizations of Markov stochastic process were analysed: the expected curve and the predicted curve. Although the definition of the predicted curve is new, curves with the same formulas are known in science as so-called deterministic models. This can be seen in the examples of the most well-known models in biology: logistics, Lotka-Volterra and Hardy-Weinberg. Attention was paid to the efficiency of calculating these both curves and their interpretation as the central tendency characteristics of Markov stochastic processes.

I S S N 2 3 4 7 -1921 V o l u m e 1 3 N u m b e r 3 J o u r n a l o f A d v a n c e i n M a t h e m a t i c s 7244 | P a g e 2 0 1 7 , J u n e h t t p s : / / c i r w o r l d . AbstractThe matrices of non-homogeneous Markov processes consist of time-dependent functions whose values at time form typical intensity matrices. For solving some problems they must be changed into stochastic matrices. A stochastic matrix for non-homogeneous Markov process consists of time-dependent functions, whose values are probabilities and it depend on assumed time period. In this paper formulas for these functions are derived. Although the formula is not simple, it allows proving some theorems for Markov stochastic processes, well known for homogeneous processes, but for non-homogeneous ones the proofs of them turned out shorter.