Article info.

ABSTRACT

Received 28 May 2018
Revised 20 Oct 2018

Accepted 29 Mar 2019

The aim of this paper is to study the model of Markov process with the state space ℤ. The applied method is similar to Depauw et al. (2009) and Lam (2014) to prove that this stochastic process converges in probability to a constant (Theorem 1.1) and to give its rate also (Theorem 3.1). Precisely, let L be the corresponding operator of the previous stochastic process and f be a given function, we solve the equation and then treat the limit of its solutions, the rate of the convergence is instantly given by the convergence of the moment of Markov process.

Keywords

Law of large numbers, Markov process, rate of convergence

Cited as: Chuong, L.H., Xuan, L.T.M., Ha, N.T.T. and Van, L.N.T., 2019. Law of large number for one dimensional Markov process. Can Tho University Journal of Science. 11(1): 95-99.