01288nas a2200145   4500000000100000000000100001008004100002260001200043100001700055700002200072700003200094245008800126490000800214520092000222       2021                            d  c12/20201 aDawid Czapla1 aKatarzyna Horbacz1 aHanna Wojewódka-Ściążko00aThe Strassen invariance principle for certain non-stationary Markov–Feller chains0 v1213 a<p>We propose certain conditions implying the functional law of the iterated logarithm (the Strassen invariance principle) for some general class of non-stationary Markov–Feller chains. This class may be briefly specified by the following two properties: firstly, the transition operator of the chain under consideration enjoys a non-linear Lyapunov-type condition, and secondly, there exists an&nbsp;appropriate Markovian coupling whose transition probability function can be decomposed into two parts, one of which is contractive and dominant in some sense. Our criterion may serve as a useful tool in verifying the functional law of the iterated logarithm for certain random dynamical systems, developed e.g. in biology and population dynamics. In the final part of the paper we present an example application of our main theorem to a mathematical model describing stochastic dynamics of gene expression.</p>