Geodesic
An ergodic theorem for additive functionals
Teoriâ veroâtnostej i ee primeneniâ, Tome 25 (1980) no. 3, pp. 625-628

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For a class of Markov processes M. Fukushima ([1]) and M. G. Sur ([2] and [3]) have proposed the description of the exceptional set in Chacon–Ornstein's theorem. In the paper a generalisation of these results for the case of additive functionals of Markov processes are given. 
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     author = {Yu. V. Direev},
     title = {An ergodic theorem for additive functionals},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {625--628},
     publisher = {mathdoc},
     volume = {25},
     number = {3},
     year = {1980},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1980_25_3_a19/}
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Yu. V. Direev. An ergodic theorem for additive functionals. Teoriâ veroâtnostej i ee primeneniâ, Tome 25 (1980) no. 3, pp. 625-628. http://geodesic.mathdoc.fr/item/TVP_1980_25_3_a19/