| Bahadur, R. R.; Ranga Rao, R. On deviations of the sample mean.
Ann. Math. Statist. 31 1960 1015--1027. MR0117775 (22 #8549) |
| Balaji, S.; Meyn, S. P. Multiplicative ergodicity and large deviations for an irreducible Markov chain.
Stochastic Process. Appl. 90 (2000), no. 1, 123--144. MR1787128 (2001h:60122) |
| Bass, Richard F.; Hsu, Pei. Some potential theory for reflecting Brownian motion in Hölder and Lipschitz domains.
Ann. Probab. 19 (1991), no. 2, 486--508. MR1106272 (92i:60142) |
| Bolthausen, Erwin. Markov process large deviations in $\tau$-topology.
Stochastic Process. Appl. 25 (1987), no. 1, 95--108. MR0904267 (88m:60073) |
| Bovier, Anton; Eckhoff, Michael; Gayrard, Véronique; Klein, Markus. Metastability and small eigenvalues in Markov chains.
J. Phys. A 33 (2000), no. 46, L447--L451. MR1804034 (2001k:82080) |
| Boyd, Stephen; Vandenberghe, Lieven. Convex optimization.
Cambridge University Press, Cambridge, 2004. xiv+716 pp. ISBN: 0-521-83378-7 MR2061575 |
| Chaganty, Narasinga Rao; Sethuraman, Jayaram. Strong large deviation and local limit theorems.
Ann. Probab. 21 (1993), no. 3, 1671--1690. MR1235434 (94i:60042) |
| Davies, E. Brian. Pseudospectra of differential operators.
J. Operator Theory 43 (2000), no. 2, 243--262. MR1753408 (2001b:47034) |
| Dawson, Donald A.; Gärtner, Jürgen. Large deviations from the McKean-Vlasov limit for weakly interacting diffusions.
Stochastics 20 (1987), no. 4, 247--308. MR0885876 (89c:60092) |
| de Acosta, A. Large deviations for empirical measures of Markov chains.
J. Theoret. Probab. 3 (1990), no. 3, 395--431. MR1057523 (91j:60051) |
| Dellnitz, Michael; Junge, Oliver. On the approximation of complicated dynamical behavior.
SIAM J. Numer. Anal. 36 (1999), no. 2, 491--515 (electronic). MR1668207 (2000c:37026) |
| Dembo, Amir; Zeitouni, Ofer. Large deviations techniques and applications.
Second edition.
Applications of Mathematics (New York), 38. Springer-Verlag, New York, 1998. xvi+396 pp. ISBN: 0-387-98406-2 MR1619036 (99d:60030) |
| Deuschel, Jean-Dominique; Stroock, Daniel W. Large deviations.
Pure and Applied Mathematics, 137. Academic Press, Inc., Boston, MA, 1989. xiv+307 pp. ISBN: 0-12-213150-9 MR0997938 (90h:60026) |
| Donsker, M. D.; Varadhan, S. R. S. Asymptotic evaluation of certain Markov process expectations for large time. I. II.
Comm. Pure Appl. Math. 28 (1975), 1--47; ibid. 28 (1975), 279--301. MR0386024 (52 #6883) |
| Donsker, M. D.; Varadhan, S. R. S. Asymptotic evaluation of certain Markov process expectations for large time. III.
Comm. Pure Appl. Math. 29 (1976), no. 4, 389--461. MR0428471 (55 #1492) |
| Donsker, M. D.; Varadhan, S. R. S. Asymptotic evaluation of certain Markov process expectations for large time. IV.
Comm. Pure Appl. Math. 36 (1983), no. 2, 183--212. MR0690656 (84h:60128) |
| Down, D.; Meyn, S. P.; Tweedie, R. L. Exponential and uniform ergodicity of Markov processes.
Ann. Probab. 23 (1995), no. 4, 1671--1691. MR1379163 (97c:60181) |
| Dupuis, Paul; Zeitouni, Ofer. A nonstandard form of the rate function for the occupation measure of a Markov chain.
Stochastic Process. Appl. 61 (1996), no. 2, 249--261. MR1386175 (97j:60048) |
| Eichelsbacher, P.; Schmock, U. Large deviations for products of empirical measures of dependent sequences.
Markov Process. Related Fields 7 (2001), no. 3, 435--468. MR1856491 (2002f:60042) |
| Feng, Jin. Martingale problems for large deviations of Markov processes.
Stochastic Process. Appl. 81 (1999), no. 2, 165--216. MR1694569 (2000j:60039) |
| Feng, Jin. Large deviations for stochastic processes.
Preprint. (2000) |
| Fleming, Wendell H. Exit probabilities and optimal stochastic control.
Appl. Math. Optim. 4 (1977/78), no. 4, 329--346. MR0512217 (80h:60100) |
| Fukushima, M.; Stroock, D. Reversibility of solutions to martingale problems.
Probability, statistical mechanics, and number theory,
107--123, Adv. Math. Suppl. Stud., 9, Academic Press, Orlando, FL, 1986. MR0875449 (88h:60140) |
| Groeneboom, P.; Oosterhoff, J.; Ruymgaart, F. H. Large deviation theorems for empirical probability measures.
Ann. Probab. 7 (1979), no. 4, 553--586. MR0537208 (80i:60030) |
| Hordijk, Arie; Spieksma, Flora. On ergodicity and recurrence properties of a Markov chain with an application to an open Jackson network.
Adv. in Appl. Probab. 24 (1992), no. 2, 343--376. MR1167263 (93i:60126) |
| Huisinga, Wilhelm; Meyn, Sean; Schütte, Christof. Phase transitions and metastability in Markovian and molecular systems.
Ann. Appl. Probab. 14 (2004), no. 1, 419--458. MR2023026 (2005b:60191) |
| Iscoe, I.; Ney, P.; Nummelin, E. Large deviations of uniformly recurrent Markov additive processes.
Adv. in Appl. Math. 6 (1985), no. 4, 373--412. MR0826590 (88b:60077) |
| Jain, Naresh C. Large deviation lower bounds for additive functionals of Markov processes.
Ann. Probab. 18 (1990), no. 3, 1071--1098. MR1062059 (91g:60037) |
| Jensen, Jens Ledet. Saddlepoint expansions for sums of Markov dependent variables on a continuous state space.
Probab. Theory Related Fields 89 (1991), no. 2, 181--199. MR1110537 (92i:60126) |
| Kartashov, N. V. Criteria for uniform ergodicity and strong stability of Markov chains with a common phase space.
(Russian) Teor. Veroyatnost. i Mat. Statist. No. 30, (1984), 65--81, 151. MR0800833 (87h:60120) |
| Kartashov, N. V.
Inequalities in theorems of ergodicity and stability for Markov chains
with a common phase space. Theor. Probability Appl. no. 30,
(1985), 247--259. |
| Kontoyiannis, I.; Meyn, S. P. Spectral theory and limit theorems for geometrically ergodic Markov processes.
Ann. Appl. Probab. 13 (2003), no. 1, 304--362. MR1952001 (2003m:60187) |
| Kunita, Hiroshi. Stochastic flows and stochastic differential equations.
Cambridge Studies in Advanced Mathematics, 24. Cambridge University Press, Cambridge, 1990. xiv+346 pp. ISBN: 0-521-35050-6 MR1070361 (91m:60107) |
| Meyn, S. P.; Tweedie, R. L. Markov chains and stochastic stability.
Communications and Control Engineering Series. Springer-Verlag London, Ltd., London, 1993. xvi+ 548 pp. ISBN: 3-540-19832-6 MR1287609 (95j:60103) |
| Meyn, Sean P.; Tweedie, R. L. Computable bounds for geometric convergence rates of Markov chains.
Ann. Appl. Probab. 4 (1994), no. 4, 981--1011. MR1304770 (95j:60106) |
| Miller, H. D. A convexivity property in the theory of random variables defined on a finite Markov chain.
Ann. Math. Statist. 32 1961 1260--1270. MR0126886 (23 #A4180) |
| Ney, P.; Nummelin, E. Markov additive processes. I. Eigenvalue properties and limit theorems.
Ann. Probab. 15 (1987), no. 2, 561--592. MR0885131 (88h:60056) |
| Ney, P.; Nummelin, E. Markov additive processes II. Large deviations.
Ann. Probab. 15 (1987), no. 2, 593--609. MR0885132 (88h:60057) |
| Nummelin, Esa. General irreducible Markov chains and nonnegative operators.
Cambridge Tracts in Mathematics, 83. Cambridge University Press, Cambridge, 1984. xi+156 pp. ISBN: 0-521-25005-6 MR0776608 (87a:60074) |
| Pinsky, Ross G. Positive harmonic functions and diffusion.
Cambridge Studies in Advanced Mathematics, 45. Cambridge University Press, Cambridge, 1995. xvi+474 pp. ISBN: 0-521-47014-5 MR1326606 (96m:60179) |
| Rey-Bellet, Luc; Thomas, Lawrence E. Asymptotic behavior of thermal nonequilibrium steady states for a driven chain of anharmonic oscillators.
Comm. Math. Phys. 215 (2000), no. 1, 1--24. MR1799873 (2001k:82061) |
| Rey-Bellet, L.; Thomas, L. E. Fluctuations of the entropy production in anharmonic chains.
Ann. Henri Poincaré 3 (2002), no. 3, 483--502. MR1915300 (2003g:82060) |
| Varadhan, S. R. S. Large deviations and applications.
CBMS-NSF Regional Conference Series in Applied Mathematics, 46. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1984. v+75 pp. ISBN: 0-89871-189-4 MR0758258 (86h:60067b) |
| Wu, Liming. Large and moderate deviations and exponential convergence for stochastic damping Hamiltonian systems.
Stochastic Process. Appl. 91 (2001), no. 2, 205--238. MR1807683 (2001m:60063) |
