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Original Articles

Moderate deviations for martingale differences and applications to φ -mixing sequences

Pages 37-64 | Published online: 29 Oct 2010

References

  • Arcones , A. 1999 . “The large deviation principle for stochastic processes” . Submitted for publication
  • Baldi , P. 1988 . “Large deviations and stochastic homogenization” . Ann. Mat. Pura Appl. , 151 : 161 – 177 .
  • Borovkov , A.A. and Mogulskii , A.A. 1978 . “Probabilities of large deviations in topological vector space I” . Sib. Math. J. , 19 : 697 – 709 .
  • Borovkov , A.A. and Mogulskii , A.A. 1980 . “Probabilities of large deviations in topological vector space II” . Sib. Math. J. , 21 : 12 – 26 .
  • Bryc , W. 1992 . “On large deviations for uniformly strong mixing sequences” . Stoch. Proc. Appl. , 41 : 191 – 202 .
  • Chen , X. 1991 . “The moderate deviations of independent vectors in Banach space” . Chin. J. Appl. Probab. Stat. , 7 : 124 – 132 .
  • Chen , X. 1999 . “Limit theorems for functionals of ergodic Markov chains with general state space” . In Memoirs of the AMS 139
  • de Acosta , A. 1997 . “Moderate deviations for empirical measures of Markov chains: lower bound” . Ann. Probab. , 25 : 259 – 284 .
  • de Acosta , A. and Chen , X. 1998 . “Moderate deviations for empirical measure of Markov chains: upper bound” . J. Theor. Probab. , 4 (11) : 75 – 110 .
  • Dembo , A. 1996 . “Moderate deviations for martingales with bounded jumps” . Elect. Comm. Probab. , 1 : 11 – 17 .
  • Dembo , A. and Zajic , T. 1997 . “Uniform large and moderate deviations for functional empirical process” . Stoch. Proc. Appl. , 67 : 195 – 211 .
  • Dembo , A. and Zeitouni , O. 1998 . Large Deviations Techniques and Applications, , 2nd Ed. , New York : Springer .
  • Djellout , H. and Guillin , A. 2001 . “Moderate deviations for Markov chains with atom” . Stoch. Proc. Appl. , In press
  • Djellout , H. and Guillin , A. 2000 . “Principe de déviations modérées pour le processus empirique fonctionnel d'une chaîne de Markov” . CRAS , 330 : 377 – 380 .
  • Doob , J.L. 1953 . Stochastic Processes , New York : Wiley .
  • Gao , F.Q. 1996 . “Moderate deviations for martingales and mixing random processes” . Stoch. Proc. Appl. , 61 : 263 – 275 .
  • Gordin , M.I. 1969 . “The central limit theorem for stationary processes” . Sov. Math. Dokl. , 10 : 1174 – 1176 .
  • Grama , I. 1997 . “On moderate deviation for martingales” . Ann. Probab. , 25 : 152 – 183 .
  • Grama , I. and Haeusler , E. 2000 . “Large deviations for martingales via Cramér's method” . Stoch. Proc. Appl. , 85 : 279 – 293 .
  • Guillin , A. 2000 . “Uniform moderate deviations of functional empirical processes of Markov chains” . Probab. Math. Statist. , 20 : 237 – 260 .
  • Hall , P. and Heyde , C.C. 1980 . Martingale Limit Theory and its Application , New York : Academic Press .
  • Jacod , J. and Shiryaev , A.N. 1987 . Limit Theorems for Stochastic Processes , Berlin : Springer .
  • Jain , N. , Jogdeo , K. and Stout , W. 1975 . “Upper and lower functions for martingales and mixing processes” . Ann. Probab. , 3 : 119 – 145 .
  • Khoshnevisan , D. 1996 . “Deviation inequalities for continuous martingales” . Stoch. Proc. Appl. , 65 : 17 – 30 .
  • Ledoux , M. 1992 . “Sur les déviations modérées des sommes de variables aléatoires vectorielles indépendantes de même loi” . Ann. Inst. H. Poincaré , 28 : 267 – 280 .
  • Liptser , R.Sh. and Shiryaev , A.N. 1989 . Theory of Martingales , Dordrecht : Kluwer Academic Publishers .
  • Puhalskii , A. 1994 . “Large deviations of semimartingales via convergence of the predictable characteristics” . Stoch. Stoch. Rep. , 49 : 27 – 85 .
  • Puhalskii , A. 1994 . “The method of stochastic exponentials for large deviations” . Stoch. Proc. Appl. , 54 : 45 – 70 .
  • Puhalskii , A. 1997 . “Large deviations of semimartingales: a maxingale problem approach. I. Limits as solutions to a maxingale problem” . Stoch. Stoch. Rep. , 61 : 141 – 243 .
  • Puhalskii , A. 1999 . “Large deviations of semimartingales a maxingale problem approach. II. Uniqueness of the maxingale problem” . Appl. Stoch. Stoch. Rep. , 68 : 65 – 143 .
  • Rackauskas , A. 1990 . “On probabilities of large deviations for martingales” . Leituvos Mathematikos Rinkinys , : 784 – 794 .
  • Rackauskas , A. 1995 . “Large deviations for martingales with some applications” . Acta Appl. Math. , 38 : 109 – 129 .
  • Revuz , D. and Yor , M. 1994 . Continuous Martingales and Brownian Motion , Berlin : Springer .
  • Worms , J. “Principes de déviations modérées pour des martingales et applications statistiques” . l'Université Marne-la-Vallée . Thése de Doctorat de
  • Wu , L. 1994 . “Large deviations, moderate deviations and LIL for empirical-processes” . Ann. Probab. , 22 : 17 – 27 .
  • Wu , L. 1995 . “Moderate deviations for dependent random variables related to CLT” . Ann. Probab. , 23 : 420 – 445 .
  • Wu , L. 1996 . “Moderate deviations for martingales and an application to uniformly mixing sequences” . In Preprint Laboratoire de Mathématiques Appliquées , Université Blaise Pascal .
  • Wu , L. 1999 . “Exponential convergence in probability for empirical means of Brownian motion and of random walks” . J. Theor. Probab. , 12 (3) : 661 – 673 .

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