×

Large deviations for functionals of stationary processes. (English) Zbl 0685.60029

Let \((S_ n)\) be a sequence of \(R^ d\)-valued random variables adapted to the internal history of a stationary sequence of random elements \((X_ n)\). We formulate conditions under which the principle of large deviations holds true for the sequence \((S_ n)\).
Reviewer: E.Nummelin

MSC:

60F10 Large deviations
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Bahadur, R.R.: Some limit theorems in statistics. SIAM, Philadelphia (1971) · Zbl 0257.62015
[2] Chernoff, H.: A measure of asymptotic efficiency for tests of a hypothesis based on the sum of observations. Ann. Math. Stat.23, 493-507 (1952) · Zbl 0048.11804
[3] Cramér, H.: Sur un nouveaux théorème-limite de la théorie des probabilités Colloquium on the theory of probability. Paris: Hermann 1938
[4] Ellis, R.S.: Large deviations and other limit theorems for a class of dependent random variables with applications to statistical mechanics (preprint, Dept. of Math., Univ. of Massachusetts 1981)
[5] Ellis, R.S.: Large deviations for a general class of random vectors. Ann. Probab.12, 1-12 (1984) · Zbl 0534.60026
[6] Ellis, R.S.: Entropy, large deviations, and statistical mechanics. Berlin Heidelberg New York: Springer 1985 · Zbl 0566.60097
[7] Gärtner, J.: On large deviations from the invariant measure. Theory Probab. Appl.22, 24-39 (1977) · Zbl 0375.60033
[8] Iscoe, I., Ney, P., Nummelin, E.: Large deviations of uniformly recurrent Markov additive process. Adv. in Appl. Math.6, 373-412 (1985) · Zbl 0602.60034
[9] Martin-Löf, A.: Mixing properties, differentiability of the free energy, and the central limit theorem for a pure phase in the Ising model at low temperature. Commun. Math. Phys.32, 75-92 (1973)
[10] Orey, S.: Large deviations in ergodic theory. In: Seminar on stochastic processes, 1984. Boston: Birkhäuser 1986 · Zbl 0585.60039
[11] Rockafellar, R.T.: Convex analysis. New Jersey: Princeton 1970 · Zbl 0193.18401
[12] Steinebach, J.: Convergence rates of large deviation probabilities in the multidimensional case. Ann. Probab.6, 751-759 (1978) · Zbl 0396.60032
[13] Varadhan, S.R.S.: Large deviations and applications. SIAM, Philadelphia (1984) · Zbl 0549.60023
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.