A Note on Comparisons of Markov Processes
O'Brien, George
Ann. Math. Statist., Tome 43 (1972) no. 6, p. 365-368 / Harvested from Project Euclid
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This note contains a simple proof of the following theorem of G. I. Kalmykov. Let $\{X_n\}$ and $\{Y_n\}$ be real-valued, discrete time Markov processes. Suppose $P(X_0 \leqq z) \leqq P(Y_0 \leqq z)$ for all real $z$ and $P(X_n \leqq z|X_{n-1} = x) \leqq P(Y_n \leqq z| Y_{n-1} = y)$ for $n = 1,2,\cdots$ and all $z$, whenever $y \leqq x$. Then $P(X_n \leqq z) \leqq P(Y_n \leqq z)$ for all $n$ and $z$. Some converse results are also given.
Publié le : 1972-02-14
Classification:  
@article{1177692734,
     author = {O'Brien, George},
     title = {A Note on Comparisons of Markov Processes},
     journal = {Ann. Math. Statist.},
     volume = {43},
     number = {6},
     year = {1972},
     pages = { 365-368},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1177692734}
}

O'Brien, George. A Note on Comparisons of Markov Processes. Ann. Math. Statist., Tome 43 (1972) no. 6, pp.  365-368. http://gdmltest.u-ga.fr/item/1177692734/