Abstract: We consider a modified Lnshnikov process as a model of a chemical polymer ization anf study the asymptotic behavior (in the thermodynamic limit;as N →∞)of a particular probability distribution on the set of N-dimensional vectors,tile kth component of which is the number of k-mers.The study study establishes the existence of three stages (subcritical,near-critical and supercritical stages)of polymerization,dependenting upon the ratio of association and dissociation rates of polymers.The present paper concentrates on the analysis of tile subcritical stage.In the subcritical.stages we show that tile size of the largest length of polymers of size N is of the order.log N as N →+∞.

Key words: Polymerization, Markov process limit behavior, stationary distribntion