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References
- Baier, U., Freidlin, M.I., Theorems on large deviations and stability under random perturbations. DAN USSR, Vol. 235, 2, (1977), 253--256. Math Review link
- Borovkov, A.A., Mogulski, A.A., Probabilities of large deviations in topological vector space, I., Siberian Math. J., Vol. 19, (1978), 697--709. Math Review link
- Borovkov, A.A., Mogulski, A.A., (1980) Probabilities of large deviations in topological vector space, II., Siberian Math. J., Vol. 19, (1980), 12--26. Math Review link
- Bhattacharya, R.N., On the functional central limit theorem and the law of the iterated logarithm for Markov processes, Z. Wharsch. verw. Geb., Vol. 60, (1982), 185--201. Math Review link
- Chen, X., The moderate deviations of independent random vectors in a Banach space, Chinese J. Appl. Probab. Statist., Vol. 7, (1991), 24--33. Math Review link
- Deushel, J.D., Stroock, D.W., Large Deviations. New York: Academic Press, (1989). Math Review link
- Donsker, M.D., Varadhan, S.R.S., Asymptotic evaluation of certain Markov process expectations for large time: I-IV, Communication of Pure and Applied Mathematics, Vol's. 28, 29, 36, (1975,76,83), 1--47, 279--301, 389--462, 183--212. Math Review links: I , II III IV
- Dembo, A., Moderate deviations for martingales with bounded jumps, Elect. Comm. in Probab., Vol. 1,(1996), 11--17. Math Review link
- Dembo, A., Zaijc, T., Uniform and moderate deviations for functional empirical processes, Stoch. Processes and their Appl., Vol. 71, (1997), 195--211. Math Review link
- Dembo, A., Zeitouni, O., Moderate deviations for iterates of expanding maps, In book: Liptser Festschrift, Singapur - New Jersey - London - Hong Kong (1998). Math Review link
- Freidlin, M.I., Averaging principle and theorem on large deviations, Uspekhi Mat., Vol. 33, (1978), 107--160. Math Review link
- Freidlin, M.I., Wentzell A.D., Random Perturbations of Dynamical Systems, N.Y. Springer, (1984). Math Review link
- Khasminskii, R.Z. , On the principle of averaging for the It^o stochastic differential equations, Kybernetika (Czechoslovakia), Vol. 4, 3, (1968), 260--279. Math Review link
- Khasminskii, R.Z., Stochastic stability of differential equations, Sijthoff & Noordhoff, (1980). Math Review link
- Ledoux, M., Sur les deviations mod'er'ees des sommes de variables al'eatoires vectorielles independantes de m^eme loi , Ann. H. Poincaré., Vol. 28, (1992), 267--280. Math Review link
- Liptser, R., Large deviations for two scaled diffusions, Theory of Probability and Related Fields, Vol. 106, (1996), 71--104. Math Review link
- Liptser, R.S., Pukhalskii, A.A., Limit theorems on large deviations for semimartingales, Stochastic and Stochastics Reports, Vol. 38, (1992), 201-249. Math Review link
- Liptser, R. and Spokoiny, V., Estimation of a dynamic function for a stochastic system with a fast component. Preprint No. 381, Weierstrass-Institut für Angewandte Analysis und Stochastik. Berlin, (1997).
- Liptser, R.Sh. and Shiryayev, A.N., Theory of Martingales.} Kluwer Acad. Publ., (1989). Math Review link
- Lynch, J., Sethuraman, J., Large deviations for the processes with independent increments, Ann. Probab., Vol. 15, (1987), 610--627. Math Review link
- Pardoux, E., Veretennikov, A.Yu., On Poisson equation and diffusion approximation, Preprint 98-14 ATP CMI Univ. de Provence, Marseille, (1998).
- Puhalskii, A.A., On functional principle of large deviations New trends in Probability and Statistics, V.Sazonov and Shervashidze (eds.), Vilnius, Lithuania, VSP/Mokslas, (1991) pp. 198--218. Math Review link
- Pukhalskii, A.A., The method of stochastic exponentials for large deviations, Stochastics Stochastic Reports, Vol. 54, 1, (1994), 45--70. Math Review link
- Skorokhod, A.V., Asymptotic Methods in the Theory of Stochastic Differential Equations, AMS, Providence Rhode Island. Translation of Mathematical Monographs, Vol. 78, (1989). Math Review link
- Varadhan, S.R.S., Large deviations and Applications, Philadelphia: SIAM, (1984). Math Review link
- Veretennikov, A. Yu., On large deviations for ergodic empirical measures, Topics in Nonparametric Estimation, Advances in Soviet Mathematics, AMS, Vol. 12, (1992), 125--133. Math Review link
- Wu, L. Moderate deviations of dependent random variables related to CLT, Ann. Probab., Vol. 23, (1995), 420--445. Math Review link

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