Large deviations of semimartingales: A maxingale problem approach i. limits as solutions to a maxingale problem

References

• de Acosta , A. 1993 . “ Exponential tightness and projective systems in large deviation theory ” . Preprint
   Google Scholar
• Akian , M. 1995 . Densities of idempotent measures and large deviations, Technical report . INRIA , 2534
   Google Scholar
• Akian , M. 1995 . Theory of cost measures: convergence of decision variables, Technical report . INRIA , 2611
   Google Scholar
• Akian , M. 1996 . On the continuity of the Cramer transform, Technical report . INRIA , 2841
   Google Scholar
• Akian , M. , Quadrat , J.-P. and Viot , M. Duality between Probability and Optimization . Proceedings of the workshop “Idempotency” . Bristol, November 1994 : Cambridge Univ. Press .
   Google Scholar
• Azencott , R. 1980 . Grandes deviations et applications . Lecture Notes Math , 114 : 1 – 176 .
   Google Scholar
• Baccelli , F. , Cohen , G. , Olsder , G. L. and Quadrat , J.-P. 1992 . “ Synchronisation and linearity: an algebra for discrete even systems ” . New York : Wiley .
   Google Scholar
• Baldi , P. 1991 . Large deviations for diffusion processes with homogenization and applications . Ann. Prob , 19 ( 2 ) : 509 – 524 .
   Google Scholar
• Baldi , P. and Chaleyat-Maurel , M. 1988 . An extension of Ventcel-Freidlin estimates . Lecture Notes Math , 1316 ( 2 ) : 305 – 327 .
   Google Scholar
• Billingsley , P. 1968 . “ Convergence of Probability Measures ” . Wiley .
   Google Scholar
• Blinovskii , Y.M. and Dobrushin , R. L. 1994 . “ Process level large deviations for a class of piecewise homogeneous random walks ” . In The Dynkin Festschrift: Markov Processes and their Applications , 1 – 59 . Boston : Birkhäuser .
   Google Scholar
• Borovkov , A. A. 1967 . Boundary-value problems for random walks and large deviations in function spaces . Th. Prob. Appl , 12 ( 4 ) : 575 – 595 .
   Google Scholar
• Bryc , W. 1990 . “ Large deviations by the asymptotic value method ” . In Diffusion processes and related problems in analysis , Edited by: Pinsky , M. 447 – 472 . Birkhäuser .
   Google Scholar
• Cutland , N. J. 1988 . An extension of the Ventcel-Freidlin large deviation principle . Stochastics , 24 : 121 – 149 .
   Google Scholar
• Dellacherie , C. 1972 . “ Capacités et Processus Stochastiques ” . Springer .
   Google Scholar
• Deuschel , J. D. and Stroock , D. W. 1989 . “ Large Deviations ” . Academic Press .
   Google Scholar
• Dinwoodie , I. H. 1993 . Identifying a large deviation rate function . Ann. Prob , 21 : 216 – 231 .
   Google Scholar
• Dobrushin , R. L. and Pechersky , E. A. Large deviations for random processes with independent increments on infinite intervals . Proc. Kolmogorov Probability and Statistics Semester . pp. 41 – 74 . Gordon and Breach .
   Google Scholar
• Dupuis , P. and Ellis , R. S. 1992 . Large deviations for Markov processes with discontinuous statistics, II: random walks . Prob. Ph. Rel. Fields , 91 : 153 – 194 .
   Google Scholar
• Dupuis , P. and Ellis , R. S. 1995 . The large deviation principle for a general class of queueing systems I Prans . Amer. Math. Soc , 347 ( 8 ) : 2689 – 2751 .
   Google Scholar
• Dupuis , P. , Ellis , R. S. and Weiss , A. 1991 . Large deviations for Markov processes with discontinuous statistics, I: General upper bounds . Ann. Prob , 19 ( 8 ) : 1280 – 1297 .
   Google Scholar
• Elliott , R. J. 1982 . “ Stochastic Calculus and Applications ” . Springer .
   Google Scholar
• Ellis , R. S. 1984 . Large deviations for a general class of random vectors . Ann. Prob , 12 ( 1 ) : 1 – 12 .
   Google Scholar
• Ethier , S. N. and Kurtz , T. G. 1986 . “ Markov Processes ” . In Characterization and Convergence , Wiley .
   Google Scholar
• Federer , H. 1969 . “ Geometric Measure Theory ” . Springer .
   Google Scholar
• Freidlin , M. I. and Wentzell , A. D. 1984 . “ Random Perturbations of Dynamical Systems (in Russian) ” . Nauka . 1979, English translation, Springer
   Google Scholar
• Friedman , A. 1976 . “ Stochastic differential equations and applications ” . Vol. 2 , Academic Press .
   Google Scholar
• Gärtner , J. 1977 . On large deviations from the invariant measure . Ph. Prob. Appl , 22 ( 1 ) : 24 – 39 .
   Google Scholar
• Ignatyuk , I. A. , Malyshev , V. and Scherbakov , V. V. 1994 . Boundary effects in large deviation problems . Russ. Math. Surv , 49 ( 2 ) : 41 – 99 .
   Google Scholar
• Ikeda , N. and Watanabe , S. 1981 . “ Stochastic Differential Equations and Diffusion Processes ” . North Holland .
   Google Scholar
• Jacod , J. and Shiryaev , A. N. 1987 . “ Limit Theorems for Stochastic Processes ” . Berlin : Springer .
   Google Scholar
• Korostelev , A. P. and Leonov , S. L. 1992 . An action functional for a diffusion process with discontinuous drift . Teor. Veroyatnost. i Primenen , 37 ( 3 ) : 570 – 576 . (in Russian), English translation: Th. Prob. Appl, 37(3), pp. 543-550
   Google Scholar
• Lindvall , T. 1973 . Weak convergence of probability measures and random functions in the function space D[0,∞) . J. Appl. Prob , 10 ( 3 ) : 109 – 121 .
   Google Scholar
• Liptser , R. Sh. and Pukhalskii , A. 1992 . Limit theorems on large deviations for semi-martingales . Stochastics , 38 ( 3 ) : 201 – 249 .
   Google Scholar
• Liptser , R. Sh. and Shiryaev , A. N. 1989 . “ Theory of Martingales ” . Kluwer .
   Google Scholar
• Lynch , J. and Sethuraman , J. 1987 . Large deviations for processes with independent increments . Ann. Prob , 15 ( 2 ) : 610 – 627 .
   Google Scholar
• Makhno , S.-Ya. 1994 . A large deviation theorem for a class of diffusion processes . Teor. Veroyatnost. i Primenen , 39 ( 3 ) : 554 – 566 . (in Russian), English translation: Th. Prob. Appl, 39(3), pp. 437-447
   Google Scholar
• Maslov , V. P. 1987 . “ Asymptotic methods of solving pseudo-differential equations ” . Nauka . (in Russian)
   Google Scholar
• Maslov , V. P. 1987 . Méthodes opératorielles . Editions Mir , (in French)
   Google Scholar
• Maslov , V. P. and Kolokoltzov , V. N. 1994 . “ Idempotent analysis and its applications to optimal control theory ” . Nauka . (in Russian)
   Google Scholar
• Meyer , P. A. 1966 . “ Probability and Potentials ” . Blaisdell .
   Google Scholar
• Micami , T. 1988 . Some generalizations of Wentzell's lower estimates on large deviations . Stochastics , 24 ( 4 ) : 269 – 284 .
   Google Scholar
• Mogulskii , A. A. 1976 . Large deviations for trajectories of multidimensional random walks . Th. Prob. Appl , 21 ( 2 ) : 300 – 315 .
   Google Scholar
• Mogulskii , A. A. 1993 . Large deviations for processes with independent increments . Ann. Prob , 21 ( 1 ) : 202 – 215 .
   Google Scholar
• Narita , K. 1988 . Large deviation principle for diffusion processes . Tsukuba J. Math , 12 ( 1 ) : 211 – 229 .
   Google Scholar
• Neveu , J. 1964 . “ Bases mathématiques du calcul des probabilityés ” . Masson et Cie
   Google Scholar
• Norberg , T. 1986 . Random capacities and their distributions . Prob. Th. Rel. Fields , 73 ( 2 ) : 281 – 297 .
   Google Scholar
• O'brien , G. L. 1995 . Sequences of capacities, with connections to large-deviation theory . Theoret. Prob , 9 ( 1 ) : 19 – 35 .
   Google Scholar
• O'brien , G. L. and Vervaat , W. 1991 . “ Capacities, large deviations and loglog laws ” . In Stable Processes and Related Topics, Progr. Prob , Edited by: Cambanis , S. , Samorodnitsky , G. and Taqqu , M. Vol. 25 , 43 – 83 . Boston, MA : Birkhäuser .
   Google Scholar
• O'brien , G. L. and Vervaat , W. 1995 . Compactness in the theory of large deviations . Stock. Proc. Appl , 57 : 1 – 10 .
   Google Scholar
• Prohorov , Yu V. 1956 . Convergence of stochastic processes and limit theorems in probability theory . Th. Prob. Appl , 1 : 157 – 214 .
   Google Scholar
• Puhalskii , A. 1991 . “ On functional principle of large deviations ” . In New Trends in Probability and Statistics, VSP/Moks'las Edited by: Sazonov , V. and Shervashidze , T. Vol. 1 , 198 – 218 .
   Google Scholar
• Puhalskii , A. A. Weak convergence theory approach to large deviations . Large deviations and applications, Workshop, Oberwolfach, 29 . Vol. 11 , pp. 16
   Google Scholar
• Puhalskii , A. 1993 . On the theory of large deviations . Th. Prob. Appl , 38 : 490 – 497 .
   Google Scholar
• Puhalskii , A. 1994 . Large deviations of semimartingales via convergence of the predictable characteristics . Stochastics , 49 : 27 – 85 .
   Google Scholar
• Puhalskii , A. 1994 . The method of stochastic exponentials for large deviations . Stock. Proc. Appl , 54 : 45 – 70 .
   Google Scholar
• Puhalskii , A. 1995 . Large deviation analysis of the single server queue . Queueing Syst , 21 : 5 – 66 .
   Google Scholar
• Puhalskii , A. and Whitt , W. 1997 . Functional large deviation principles for first passage time processes . Ann. Appl. Prob , 21 (to appear)
   Google Scholar
• Remillard , B. and Dawson , D. A. 1989 . Laws of the iterated logarithm and large deviations for a class of diffusion processes . Canad. J. Statist , 17 ( 4 ) : 349 – 376 .
   Google Scholar
• Skorohod , A. V. 1956 . Limit theorems for stochastic processes . Th. Prob. Appl , 1 ( 4 ) : 261 – 292 .
   Google Scholar
• Varadhan , S. R. S. 1966 . Asymptotic probabilities and differential equations . Comm. Pure. Appl. Math , 19 ( 3 ) : 261 – 286 .
   Google Scholar
• Varadhan , S. R. S. 1984 . Large Deviations and Applications . Siam , 19 ( 3 )
   Google Scholar
• Vervaat , W. 1988 . Narrow and vague convergence of set functions . Statist. & Prob. Lett , 6 ( 5 ) : 295 – 298 .
   Google Scholar
• Wentzell , A. D. 1989 . “ Limit Theorems on Large Deviations for Markov Random Processes ” . In English translation , Reidel : Nauka . (in Russian)
   Google Scholar
• Whitt , W. 1980 . Some useful functions for functional limit theorems . Math. Oper. Res , 5 ( 1 ) : 67 – 85 .
   Google Scholar