Geodesic
Local limit theorems for functions of random fields
Zapiski Nauchnykh Seminarov POMI, Studies in mathematical statistics. Part VI, Tome 136 (1984), pp. 168-182

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Sufficient conditions are obtained for the convergence in variation of the sequences of distributions for some class of functionals defined on the random fields. 
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     author = {N. V. Smorodina},
     title = {Local limit theorems for functions of random fields},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {168--182},
     publisher = {mathdoc},
     volume = {136},
     year = {1984},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_1984_136_a13/}
}
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N. V. Smorodina. Local limit theorems for functions of random fields. Zapiski Nauchnykh Seminarov POMI, Studies in mathematical statistics. Part VI, Tome 136 (1984), pp. 168-182. http://geodesic.mathdoc.fr/item/ZNSL_1984_136_a13/