On the asymptotic behaviors of time homogeneous Markov chains in two-inertia systems

In this study, we construct a time homogeneous Markov chain considering both friction and probability. By investigating , we would like to observe the stability and/or the asymptotic behavior of a two inertia system. Assume that and are frictionless stochastic processes driven by , where is an indeterminate parameter, and are mutual independent 1-dim Levy processes. Let , and be positive dead zone gaps, and . The research has three purposes. The first one is to probe the asymptotic behaviors of and . The second one is to probe the asymptotic behaviors of . The third one is to compare the relationship among , , and . Our results are as follows. (1) The asymptotic behaviors of both processes are determined by and . (2) The time homogeneous Markov chain possesses the limit distribution. (3) and possess the limit distributions, respectively. However, by means of our results, and do not have limits in certain conditions.