Approximation of bivariate Markov chains by one-dimensional diffusion processes
Applications of Mathematics, Tome 23 (1978) no. 4, pp. 267-279.

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The paper deals with several questions of the diffusion approximation. The goal of this paper is to create the general method of reducting the dimension of the model with the aid of the diffusion approximation. Especially, two dimensional random variables are approximated by one-dimensional diffusion process by replacing one of its coordinates by a certain characteristic, e.g. by its stationary expectation. The suggested method is used for several different systems. For instance, the method is applicable to the sequences of Markov chains $\left\{(^nX_m, ^nY_m), m=0,1,\ldots \right\}\ n=1,2,\ldots$ where the tendency of $\left\{^nY_m \right\}$ to the stationary state is greater than that of $\left\{^nX_m\right\}$.
DOI : 10.21136/AM.1978.103752
Classification : 60F05, 60H10, 60J05, 60J60, 60K05
Mots-clés : diffusion approximation; Markov chains; ito equation; difference equation; renewal process 
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     title = {Approximation of bivariate {Markov} chains by one-dimensional diffusion processes},
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Kuklíková, Daniela. Approximation of bivariate Markov chains by one-dimensional diffusion processes. Applications of Mathematics, Tome 23 (1978) no. 4, pp. 267-279. doi : 10.21136/AM.1978.103752. https://geodesic-test.mathdoc.fr/articles/10.21136/AM.1978.103752/

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