Law of large number for one dimensional Markov process
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* Corresponding author (lhchuong@ctu.edu.vn)
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Received:
28 May 2018
Revised:
20 Oct 2018
Accepted:
29 Mar 2019
Published:
30 Mar 2019
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How to Cite
Lam, H. C., Le, T. M. X., Le, N. T. V., & Nguyen, T. T. H. (2019). Law of large number for one dimensional Markov process. CTU Journal of Innovation and Sustainable Development , 11(1), 95-99. https://doi.org/10.22144/ctu.jen.2019.013
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Abstract
The aim of this paper is to study the model of Markov process with the state space ℤ. We apply the method 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
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References
Depauw, J. and Derrien, J.M., 2009. Variance limite d'une marche aléatoire réversible en milieu aléatoire sur Z. Comptes Rendus Mathematique, 347(7-8): 401-406.
Lam, H.C., 2014. A quenched central limit theorem for reversible random walks in a random environment on Z. Journal of Applied Probability, 51(4): 1051-1064.
Ross, S. M., 2010. Introduction to Probability Models. Elsevier Inc, 782 pages.