This is a preview of subscription content, log in via an institution to check access.
Literature Cited
V. A. Malyshev, “Cluster expansions in lattice models of statistical physics and quantum field theory,” Usp. Mat. Nauk.35, No. 2 (212), 3–55 (1980).
V. A. Malyshev, “Elementary introduction to the mathematical physics of infinite-partial systems,” Lektsii dlya Molodykh Uchenykh, Vol. 27, Dubna (1983).
H. Cramer, “A new limit theorem of probability theory,” Usp. Mat. Nauk,10, 166–178 (1944).
V. V. Petrov, “Generalization of Cramer's limit theorem,” Usp. Mat. Nauk, No. 4, 195–202 (1954).
W. Feller, “Generalization of a probability limit theorem of Cramer,” Trans. Am. Math. Soc.,54, No. 3, 361–372 (1943).
V. V. Petrov, “Large deviations of sums of random variables,” Vestn. Leningr. Gos. Univ., No. 1, 25–37 (1961).
V. V. Petrov, “Asymptotic behavior of probabilities of large deviations,” Teor. Veroyatn. Primen.,13, No. 3, 432–444 (1968).
V. A. Statulevicius, “On large deviations,” Z. Wahr. Verw. Geb.,6, No. 2, 133–144 (1966).
V. V. Petrov, Sums of Independent Random Variables, Springer-Verlag (1975).
S. V. Nagaev, “Improvement of limit theorems for homogeneous Markov chains,” Teor. Veroyatn. Primen.,6, No. 1, 67–86 (1967).
L. Saulis and V. Statulyavichus, “Large deviations in the scheme of summation of random variables with weights,” Liet. Mat. Rinkinys,16, No. 2, 146–154 (1976).
W. Wolf, “Einige grenzwertsätze für grosse Abweichungen II,” Wissenschaftl. Zeitschrift Technischen Universität. Dresden,21, No. 4, 771–779 (1972).
S. A. Book, “Large deviations probabilities for weighted sums,” Z. Wahr. Verw. Geb.,26, 43–49 (1973).
S. A. Book, “Large deviations probabilities for weighted sums,” Ann. Math. Statistics,43, 1221–1234 (1972).
V. A. Statulyavichus, “Limit theorems for sums of random variables connected in a Markov chain,” Liet. Mat. Rinkinys,9, No. 2, 345–362 (1969);16, No. 3, 635–672 (1969);10, No. 1, 161–169 (1970).
V. A. Statulyavichus, “Limit theorems for random functions,” Liet. Mat. Rinkinys,10, No. 1, 161–169 (1970).
V. A. Statulyavichus, “Theorems of large deviations for sums of dependent random variables,” Liet. Mat. Rinkinys,19, No. 2, 200–208 (1979).
A. É. Plikusas, “Large deviations for certain nonlinear transformations of a stationary Gaussian process,” Dokl. Akad Nauk SSSR,242, No. 1, 773–776 (1978).
R. Rudzikis, L. Saulis, and V. Statulyavichus, “General lemma on probabilities of large deviations,” Liet. Mat. Rinkinys,18, No. 2, 99–116 (1978).
H. A. Chernoff, “Measure of asymptotic efficiency for tests of a hypothesis based on sums of observations,” Ann. Math. Statist.,23, 493–507 (1952).
B. Riauba, “On large deviations,” in: Abstracts of Communications. Fourth USSR-Japan Sumposium on Probability Theory and Mathematical Statistics, Vol. 2, Tbilisi (1982).
P. P. Gudinas, “Large deviations of order for sums of random variables, connected in a homogeneous Markov chain,” Liet. Mat. Rinkinys,21, No. 4, 65–74 (1981).
D. Ruelle, Statistical Mechanics (Rigorous Results) [Russian translation], Mir, Moscow (1971).
Additional information
Institute of Mathematics and Cybernetics, Academy of Sciences of the Lithuanian SSR. Translated from Litovskii Matematicheskii Sbornik (Lietuvos Matematikos Rinkinys), Vol. 25, No. 4, pp. 164–176, October–December, 1985.
Rights and permissions
About this article
Cite this article
Čepulėnas, S. Probabilities of large deviations for random fields. Lith Math J 25, 381–390 (1985). https://doi.org/10.1007/BF00968336
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00968336