메뉴 건너뛰기




Volumn 10, Issue , 2005, Pages 61-123

Large deviations asymptotics and the spectral theory of multiplicatively regular markov processes

Author keywords

Empirical measures; Entropy; Large deviations; Large deviations principle; Markov process; Nonlinear generator; Stochastic Lyapunov function

Indexed keywords


EID: 15944385310     PISSN: None     EISSN: 10836489     Source Type: Journal    
DOI: 10.1214/EJP.v10-231     Document Type: Article
Times cited : (124)

References (45)
  • 1
    • 0001505964 scopus 로고
    • On deviations of the sample mean
    • R.R. Bahadur and R. Ranga Rao. On deviations of the sample mean. Ann. Math. Statist., 31:1015-1027, 1960.
    • (1960) Ann. Math. Statist , vol.31 , pp. 1015-1027
    • Bahadur, R.R.1    Ranga Rao, R.2
  • 2
    • 0002801896 scopus 로고    scopus 로고
    • Multiplicative ergodicity and large deviations for an irreducible Markov chain
    • S. Balaji and S.P. Meyn. Multiplicative ergodicity and large deviations for an irreducible Markov chain. Stochastic Process. Appl., 90(1):123-144, 2000.
    • (2000) Stochastic Process. Appl , vol.90 , Issue.1 , pp. 123-144
    • Balaji, S.1    Meyn, S.P.2
  • 3
    • 0001584203 scopus 로고
    • Some potential theory for reflecting Brownian motion in Holder and Lipschitz domains
    • R.F. Bass and P. Hsu. Some potential theory for reflecting Brownian motion in Holder and Lipschitz domains. Ann. Probab., 19(2):486-508, 1991.
    • (1991) Ann. Probab , vol.19 , Issue.2 , pp. 486-508
    • Bass, R.F.1    Hsu, P.2
  • 4
    • 0040632820 scopus 로고
    • Markov process large deviations in t-topology
    • E. Bolthausen. Markov process large deviations in t-topology. Stochastic Process. Appl., 25(1):95-108, 1987.
    • (1987) Stochastic Process. Appl , vol.25 , Issue.1 , pp. 95-108
    • Bolthausen, E.1
  • 5
    • 0034711194 scopus 로고    scopus 로고
    • Metastability and small eigenvalues in Markov chains
    • A. Bovier, M. Eckhoff, V. Gayrard, and M. Klein. Metastability and small eigenvalues in Markov chains. J. Phys. A, 33(46):L447-L451, 2000.
    • (2000) J. Phys. A , vol.33 , Issue.46 , pp. L447-L451
    • Bovier, A.1    Eckhoff, M.2    Gayrard, V.3    Klein, M.4
  • 6
    • 0004055894 scopus 로고    scopus 로고
    • preparation, Department of Electrical Engineering, Stanford University
    • S. Boyd and L. Vandenberghe. Convex Optimization. In preparation, Department of Electrical Engineering, Stanford University, 2002.
    • (2002) Convex Optimization
    • Boyd, S.1    Vandenberghe, L.2
  • 7
    • 0001053010 scopus 로고
    • Strong large deviation and local limit theorems
    • N.R. Chaganty and J. Sethuraman. Strong large deviation and local limit theorems. Ann. Probab., 21(3):1671-1690, 1993.
    • (1993) Ann. Probab , vol.21 , Issue.3 , pp. 1671-1690
    • Chaganty, N.R.1    Sethuraman, J.2
  • 8
    • 0001316461 scopus 로고    scopus 로고
    • Pseudospectra of differential operators
    • E.B. Davies. Pseudospectra of differential operators. J. Operator Theory, 43:243-262, 2000.
    • (2000) J. Operator Theory , vol.43 , pp. 243-262
    • Davies, E.B.1
  • 9
    • 0001356070 scopus 로고
    • Large deviations from the McKean-Vlasov limit for weakly interacting diffusions
    • D.A. Dawson and J. Gartner. Large deviations from the McKean-Vlasov limit for weakly interacting diffusions. Stochastics, 20(4):247-308, 1987.
    • (1987) Stochastics , vol.20 , Issue.4 , pp. 247-308
    • Dawson, D.A.1    Gartner, J.2
  • 10
    • 0011692844 scopus 로고
    • Large deviations for empirical measures of Markov chains
    • A. de Acosta. Large deviations for empirical measures of Markov chains. J. Theoret. Probab., 3(3):395-431, 1990.
    • (1990) J. Theoret. Probab , vol.3 , Issue.3 , pp. 395-431
    • De Acosta, A.1
  • 11
    • 0000371241 scopus 로고    scopus 로고
    • On the approximation of complicated dynamical behavior
    • Michael Dellnitz and Oliver Junge. On the approximation of complicated dynamical behavior. SIAM J. On Numerical Analysis, 36(2):491-515, 1999.
    • (1999) SIAM J. On Numerical Analysis , vol.36 , Issue.2 , pp. 491-515
    • Dellnitz, M.1    Junge, O.2
  • 14
    • 84980178612 scopus 로고    scopus 로고
    • Asymptotic evaluation of certain Markov process expectations for large time. I. II
    • M.D. Donsker and S.R.S. Varadhan. Asymptotic evaluation of certain Markov process expectations for large time. I. II. Comm. Pure Appl. Math., 28:1-47;
    • Comm. Pure Appl. Math , vol.28 , pp. 1-47
    • Donsker, M.D.1    Varadhan, S.R.S.2
  • 15
    • 84980140517 scopus 로고
    • Asymptotic evaluation of certain Markov process expectations for large time. I. II
    • 1975
    • M.D. Donsker and S.R.S. Varadhan. Asymptotic evaluation of certain Markov process expectations for large time. I. II. Comm. Pure Appl. Math.,28 (1975), 279-301, 1975.
    • (1975) Comm. Pure Appl. Math , vol.28 , pp. 279-301
    • Donsker, M.D.1    Varadhan, S.R.S.2
  • 16
    • 84980151353 scopus 로고
    • Asymptotic evaluation of certain Markov process expectations for large time. III
    • M.D. Donsker and S.R.S. Varadhan. Asymptotic evaluation of certain Markov process expectations for large time. III. Comm. Pure Appl. Math., 29(4):389-461, 1976.
    • (1976) Comm. Pure Appl. Math , vol.29 , Issue.4 , pp. 389-461
    • Donsker, M.D.1    Varadhan, S.R.S.2
  • 17
    • 84990587390 scopus 로고
    • Asymptotic evaluation of certain Markov process expectations for large time. IV
    • M.D. Donsker and S.R.S. Varadhan. Asymptotic evaluation of certain Markov process expectations for large time. IV. Comm. Pure Appl. Math., 36(2):183-212, 1983.
    • (1983) Comm. Pure Appl. Math , vol.36 , Issue.2 , pp. 183-212
    • Donsker, M.D.1    Varadhan, S.R.S.2
  • 18
    • 21344460828 scopus 로고
    • Exponential and uniform ergodicity of Markov processes
    • D. Down, S. P. Meyn, and R. L. Tweedie. Exponential and uniform ergodicity of Markov processes. Ann. Probab., 23(4):1671-1691, 1995.
    • (1995) Ann. Probab , vol.23 , Issue.4 , pp. 1671-1691
    • Down, D.1    Meyn, S.P.2    Tweedie, R.L.3
  • 19
    • 0030079492 scopus 로고    scopus 로고
    • A nonstandard form of the rate function for the occupation measure of a markov chain
    • P. Dupuis and O. Zeitouni. A nonstandard form of the rate function for the occupation measure of a markov chain. Stochastic Process. Appl., 61:249-261, 1996.
    • (1996) Stochastic Process. Appl , vol.61 , pp. 249-261
    • Dupuis, P.1    Zeitouni, O.2
  • 20
    • 0009955236 scopus 로고    scopus 로고
    • Large deviations for products of empirical measures of dependent sequences
    • P. Eichelsbacher and U. Schmock. Large deviations for products of empirical measures of dependent sequences. Markov Process. Related Fields, 7(3):435-468, 2001.
    • (2001) Markov Process. Related Fields , vol.7 , Issue.3 , pp. 435-468
    • Eichelsbacher, P.1    Schmock, U.2
  • 21
    • 0033147724 scopus 로고    scopus 로고
    • Martingale problems for large deviations of Markov processes
    • J. Feng. Martingale problems for large deviations of Markov processes. Stochastic Process. Appl., 81:165-212, 1999.
    • (1999) Stochastic Process. Appl , vol.81 , pp. 165-212
    • Feng, J.1
  • 23
    • 0018156010 scopus 로고
    • Exit probabilities and optimal stochastic control
    • W.H. Fleming. Exit probabilities and optimal stochastic control. App. Math. Optim., 4:329-346, 1978.
    • (1978) App. Math. Optim , vol.4 , pp. 329-346
    • Fleming, W.H.1
  • 25
    • 0001005608 scopus 로고
    • Large deviation theorems for empirical probability measures
    • P. Groeneboom, J. Oosterhoff, and F.H. Ruymgaart. Large deviation theorems for empirical probability measures. Ann. Probab., 7(4):553-586, 1979.
    • (1979) Ann. Probab , vol.7 , Issue.4 , pp. 553-586
    • Groeneboom, P.1    Oosterhoff, J.2    Ruymgaart, F.H.3
  • 26
    • 0001144425 scopus 로고    scopus 로고
    • On ergodicity and recurrence properties of a Markov chain with an application to an open Jackson network
    • A. Hordijk and F. Spieksma. On ergodicity and recurrence properties of a Markov chain with an application to an open Jackson network. Adv. in Appl. Probab., 24(2):343-376, 1992.
    • Adv. In Appl. Probab , vol.24 , Issue.2 , pp. 343-376
    • Hordijk, A.1    Spieksma, F.2
  • 27
    • 15944402414 scopus 로고    scopus 로고
    • Phase transitions and metastability in Markovian and molecular systems
    • to appear
    • W. Huisinga, S.P. Meyn, and C. Schuette. Phase transitions and metastability in Markovian and molecular systems. Ann. Appl. Probab., 2001. to appear.
    • (2001) Ann. Appl. Probab
    • Huisinga, W.1    Meyn, S.P.2    Schuette, C.3
  • 28
    • 0000269609 scopus 로고
    • Large deviations of uniformly recurrent Markov additive processes
    • I. Iscoe, P. Ney, and E. Nummelin. Large deviations of uniformly recurrent Markov additive processes. Adv. Appl. Math., 6:373-412, 1985.
    • (1985) Adv. Appl. Math , vol.6 , pp. 373-412
    • Iscoe, I.1    Ney, P.2    Nummelin, E.3
  • 29
    • 0038992289 scopus 로고
    • Large deviation lower bounds for additive functionals of Markov processes
    • N.C. Jain. Large deviation lower bounds for additive functionals of Markov processes. Ann. Probab, 18(3):1071-1098, 1990.
    • (1990) Ann. Probab , vol.18 , Issue.3 , pp. 1071-1098
    • Jain, N.C.1
  • 30
    • 0001740568 scopus 로고
    • Saddlepoint expansions for sums of Markov dependent variables on a continuous state space
    • J.L. Jensen. Saddlepoint expansions for sums of Markov dependent variables on a continuous state space. Probab. Theory Related Fields, 89(2):181-199, 1991.
    • (1991) Probab. Theory Related Fields , vol.89 , Issue.2 , pp. 181-199
    • Jensen, J.L.1
  • 31
    • 0038876647 scopus 로고
    • Criteria for uniform ergodicity and strong stability of Markov chains with a common phase space
    • N.V. Kartashov. Criteria for uniform ergodicity and strong stability of Markov chains with a common phase space. Theor. Probability Appl., 30:71-89, 1985.
    • (1985) Theor. Probability Appl , vol.30 , pp. 71-89
    • Kartashov, N.V.1
  • 32
    • 0040061152 scopus 로고
    • Inequalities in theorems of ergodicity and stability for Markov chains with a common phase space
    • N.V. Kartashov. Inequalities in theorems of ergodicity and stability for Markov chains with a common phase space. Theor. Probability Appl., 30:247-259, 1985.
    • (1985) Theor. Probability Appl , vol.30 , pp. 247-259
    • Kartashov, N.V.1
  • 33
    • 0037279497 scopus 로고    scopus 로고
    • Spectral theory and limit theorems for geometrically ergodic Markov processes
    • I. Kontoyiannis and S.P. Meyn. Spectral theory and limit theorems for geometrically ergodic Markov processes. Ann. Appl. Probab., 13:304-362, February 2003.
    • (2003) Ann. Appl. Probab , vol.13 , pp. 304-362
    • Kontoyiannis, I.1    Meyn, S.P.2
  • 36
    • 0000566364 scopus 로고
    • Computable bounds for geometric convergence rates of Markov chains
    • S.P. Meyn and R.L. Tweedie. Computable bounds for geometric convergence rates of Markov chains. Ann. Appl. Probab., 4(4):981-1011, 1994.
    • (1994) Ann. Appl. Probab , vol.4 , Issue.4 , pp. 981-1011
    • Meyn, S.P.1    Tweedie, R.L.2
  • 37
    • 0000413365 scopus 로고
    • A convexivity property in the theory of random variables defined on a finite Markov chain
    • H.D. Miller. A convexivity property in the theory of random variables defined on a finite Markov chain. Ann. Math. Statist., 32:1260-1270, 1961.
    • (1961) Ann. Math. Statist , vol.32 , pp. 1260-1270
    • Miller, H.D.1
  • 38
    • 0001621270 scopus 로고
    • Markov additive processes. I. Eigenvalue properties and limit theorems
    • P. Ney and E. Nummelin. Markov additive processes. I. Eigenvalue properties and limit theorems. Ann. Probab., 15(2):561-592, 1987.
    • (1987) Ann. Probab , vol.15 , Issue.2 , pp. 561-592
    • Ney, P.1    Nummelin, E.2
  • 39
    • 0001621270 scopus 로고
    • Markov additive processes II. Large deviations
    • P. Ney and E. Nummelin. Markov additive processes II. Large deviations. Ann. Probab., 15(2):593-609, 1987.
    • (1987) Ann. Probab , vol.15 , Issue.2 , pp. 593-609
    • Ney, P.1    Nummelin, E.2
  • 42
    • 0034336318 scopus 로고    scopus 로고
    • Asymptotic behavior of thermal nonequilibrium steady states for a driven chain of anharmonic oscillators
    • L. Rey-Bellet and L. E. Thomas. Asymptotic behavior of thermal nonequilibrium steady states for a driven chain of anharmonic oscillators. Comm. Math. Phys., 215:1-24, 2000.
    • (2000) Comm. Math. Phys , vol.215 , pp. 1-24
    • Rey-Bellet, L.1    Thomas, L.E.2
  • 43
    • 0036435161 scopus 로고    scopus 로고
    • Fluctuations of the entropy production in anharmonic chains
    • L. Rey-Bellet and L. E. Thomas. Fluctuations of the entropy production in anharmonic chains. Ann. Henri Poincaré, 3(3):483-502, 2002.
    • (2002) Ann. Henri Poincaré , vol.3 , Issue.3 , pp. 483-502
    • Rey-Bellet, L.1    Thomas, L.E.2
  • 44
    • 0004082897 scopus 로고
    • Society for Industrial and Applied Mathematics (SIAM), Philadelphia, Pa
    • S.R.S. Varadhan. Large Deviations and Applications. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, Pa., 1984.
    • (1984) Large Deviations and Applications
    • Varadhan, S.R.S.1
  • 45
    • 0012871505 scopus 로고    scopus 로고
    • Large and moderate deviations and exponential convergence for stochastic damping Hamiltonian systems
    • L. Wu. Large and moderate deviations and exponential convergence for stochastic damping Hamiltonian systems. Stochastic Process. Appl., 91(2):205-238, 2001.
    • (2001) Stochastic Process. Appl , vol.91 , Issue.2 , pp. 205-238
    • Wu, L.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.