메뉴 건너뛰기




Volumn 36, Issue 4, 2008, Pages 1390-1420

Large deviations for infinite dimensional stochastic dynamical systems

Author keywords

Brownian sheet; Freidlin Wentzell LDP; Infinite dimensional Brownian motion; Large deviations; Small noise asymptotics; Stochastic evolution equations; Stochastic partial differential equations

Indexed keywords


EID: 52049112983     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/07-AOP362     Document Type: Article
Times cited : (294)

References (30)
  • 1
    • 52049125290 scopus 로고    scopus 로고
    • AZENCOTT, R. (.1980). Grandes deviations et applications. École d'Été de Probabilités de Saint-Flour VII. Lecture Notes in Math. 774 1-176. Springer, Berlin. MR0590626
    • AZENCOTT, R. (.1980). Grandes deviations et applications. École d'Été de Probabilités de Saint-Flour VII. Lecture Notes in Math. 774 1-176. Springer, Berlin. MR0590626
  • 2
    • 0033228798 scopus 로고    scopus 로고
    • Large deviations for Burger's type SPDE
    • MR1720097
    • CARDON-WEBBER, C. (1999). Large deviations for Burger's type SPDE. Stochastic Process. Appl. 84 53-70. MR1720097
    • (1999) Stochastic Process. Appl , vol.84 , pp. 53-70
    • CARDON-WEBBER, C.1
  • 3
    • 18844410951 scopus 로고    scopus 로고
    • A variational representation for positive functional of infinite dimensional Brownian motions
    • MR1785237
    • BUDHIRAJA, A. and DIJPUIS, P. (2000). A variational representation for positive functional of infinite dimensional Brownian motions. Probab. Math. Statist. 20 39-61. MR1785237
    • (2000) Probab. Math. Statist , vol.20 , pp. 39-61
    • BUDHIRAJA, A.1    DIJPUIS, P.2
  • 4
    • 2142772793 scopus 로고    scopus 로고
    • Large deviations for stochastic reaction-diffusion systems with multiplicative noise and non-Lipschitz reaction term
    • MR2044675
    • CERRAI, S. and ROCKNER, M. (2004). Large deviations for stochastic reaction-diffusion systems with multiplicative noise and non-Lipschitz reaction term. Ann. Probab. 32 1100-1139. MR2044675
    • (2004) Ann. Probab , vol.32 , pp. 1100-1139
    • CERRAI, S.1    ROCKNER, M.2
  • 5
    • 0031574565 scopus 로고    scopus 로고
    • Uniform large deviations for parabolic SPDEs and applications
    • MR1486551
    • CHENAL, F. and MILLET, A. (1997). Uniform large deviations for parabolic SPDEs and applications. Stochastic Process. Appl. 72 161-187. MR1486551.
    • (1997) Stochastic Process. Appl , vol.72 , pp. 161-187
    • CHENAL, F.1    MILLET, A.2
  • 6
    • 84990627145 scopus 로고
    • Large deviation problem for some parabolic Itô equations
    • MR1135925
    • CHOW, P. L. (1992). Large deviation problem for some parabolic Itô equations. Comm. Pure Appl. Math. 45 97-120. MR1135925
    • (1992) Comm. Pure Appl. Math , vol.45 , pp. 97-120
    • CHOW, P.L.1
  • 7
    • 52049093498 scopus 로고    scopus 로고
    • DA PRATO, G. and ZABCYK, J. (1992). Stochastic Equations in Infinite Dimensions. Cambridge Univ. Press. MR1207136
    • DA PRATO, G. and ZABCYK, J. (1992). Stochastic Equations in Infinite Dimensions. Cambridge Univ. Press. MR1207136
  • 8
    • 52049090181 scopus 로고    scopus 로고
    • DUPUIS, P. and ELLIS, R. (1997). A Weak Convergence Approach to the Theory of Large Deviations. Wiley, New York. MR1431744
    • DUPUIS, P. and ELLIS, R. (1997). A Weak Convergence Approach to the Theory of Large Deviations. Wiley, New York. MR1431744
  • 9
    • 0000754401 scopus 로고
    • Large fluctuations for a nonlinear heat equation with noise
    • MR0684578
    • FARIS, W. G. and JONAS-LASINO, G. (1982). Large fluctuations for a nonlinear heat equation with noise. J. Phys. A 15 3025-3055. MR0684578
    • (1982) J. Phys. A , vol.15 , pp. 3025-3055
    • FARIS, W.G.1    JONAS-LASINO, G.2
  • 10
    • 33644956853 scopus 로고    scopus 로고
    • Large deviations for diffusion and Hamilton-Jacobi equation in Hubert space
    • MR2206350
    • FENG, J. (2006). Large deviations for diffusion and Hamilton-Jacobi equation in Hubert space. Ann. Probab. 34 321-385. MR2206350
    • (2006) Ann. Probab , vol.34 , pp. 321-385
    • FENG, J.1
  • 11
    • 52049087870 scopus 로고    scopus 로고
    • FENG, J. and KURTZ, T. G. (2006). Large Deviations of Stochastic Processes. Amer. Math. Soc., Providence, RI. MR2260560
    • FENG, J. and KURTZ, T. G. (2006). Large Deviations of Stochastic Processes. Amer. Math. Soc., Providence, RI. MR2260560
  • 12
    • 0000588313 scopus 로고
    • Random perturbations of reaction-diffusion equations: The quasi deterministic approximation
    • MR0924775
    • FREIDLIN, M. (1988). Random perturbations of reaction-diffusion equations: The quasi deterministic approximation. Trans. Amer. Math. Soc. 305 665-697. MR0924775
    • (1988) Trans. Amer. Math. Soc , vol.305 , pp. 665-697
    • FREIDLIN, M.1
  • 13
    • 52049101838 scopus 로고    scopus 로고
    • FREIDLIN, M. I. and WENTZELL, A.D. (1984). Random Perturbations of Dynamical Systems. Springer, New York. MR0722136
    • FREIDLIN, M. I. and WENTZELL, A.D. (1984). Random Perturbations of Dynamical Systems. Springer, New York. MR0722136
  • 14
    • 52049105423 scopus 로고    scopus 로고
    • GARSIA, A. (1972). Continuity properties of Gaussian processes with multidimensional time parameter. Proc. Sixth Berkeley Symp. Math. Statist. Probab. 2 369-374. Univ. California Press, Berkeley. MR0410880
    • GARSIA, A. (1972). Continuity properties of Gaussian processes with multidimensional time parameter. Proc. Sixth Berkeley Symp. Math. Statist. Probab. 2 369-374. Univ. California Press, Berkeley. MR0410880
  • 15
    • 0007158715 scopus 로고
    • On smoothness conditions for trajectories of random functions
    • MR0700208
    • IBRAGIMOV, I. (1983). On smoothness conditions for trajectories of random functions. Theory Probab. Appl. 28 240-262. MR0700208
    • (1983) Theory Probab. Appl , vol.28 , pp. 240-262
    • IBRAGIMOV, I.1
  • 16
    • 52049115696 scopus 로고
    • Large deviations of solutions of nonlinear stochastic equations
    • MR0961434
    • IMAUIKIN, V. and KOMECH, A. I. (1988). Large deviations of solutions of nonlinear stochastic equations. Trudy Sem. Petrovsk. 13 177-196. MR0961434
    • (1988) Trudy Sem. Petrovsk , vol.13 , pp. 177-196
    • IMAUIKIN, V.1    KOMECH, A.I.2
  • 17
    • 52049084639 scopus 로고    scopus 로고
    • KALLENBERG, O. (2002). Foundations of Modern Probability, 2nd ed. Springer, New York. MR1876169
    • KALLENBERG, O. (2002). Foundations of Modern Probability, 2nd ed. Springer, New York. MR1876169
  • 18
    • 52049084389 scopus 로고    scopus 로고
    • KALLIANPUR, G. and XIONG, J. (1995). Stochastic Differential Equations in InfiniteDimensional Spaces. IMS, Hayward, CA. MR1465436
    • KALLIANPUR, G. and XIONG, J. (1995). Stochastic Differential Equations in InfiniteDimensional Spaces. IMS, Hayward, CA. MR1465436
  • 19
    • 0030486147 scopus 로고    scopus 로고
    • Large deviations for a class of stochastic partial differential equations
    • MR1387638
    • KALLIANPUR, G. and XIONG, J. (1996). Large deviations for a class of stochastic partial differential equations. Ann. Probab. 24 320-345. MR1387638
    • (1996) Ann. Probab , vol.24 , pp. 320-345
    • KALLIANPUR, G.1    XIONG, J.2
  • 20
    • 0001321966 scopus 로고
    • Existence, uniqueness and smoothness for a class of function valued stochastic partial differential equations
    • MR1275582
    • KOTELENEZ, P. (1992). Existence, uniqueness and smoothness for a class of function valued stochastic partial differential equations. Stochastics Stochastics Rep. 41 177-199. MR1275582
    • (1992) Stochastics Stochastics Rep , vol.41 , pp. 177-199
    • KOTELENEZ, P.1
  • 21
    • 52049104493 scopus 로고    scopus 로고
    • KIJSHNER, H. J. and DUPUIS, P. (1992). Numerical Methods for Stochastic Control Problems in Continuous Time. Springer, New York. MR1217486
    • KIJSHNER, H. J. and DUPUIS, P. (1992). Numerical Methods for Stochastic Control Problems in Continuous Time. Springer, New York. MR1217486
  • 22
    • 21344489559 scopus 로고
    • Large deviation estimates for stochastic evolution equations
    • MR1254827
    • PESZAT, S. (1994). Large deviation estimates for stochastic evolution equations. Probab. Theory Related Fields 98 113-136. MR1254827
    • (1994) Probab. Theory Related Fields , vol.98 , pp. 113-136
    • PESZAT, S.1
  • 23
    • 18844384199 scopus 로고    scopus 로고
    • Schilder theorem for the Brownian motion on the diffeomorphism group of the circle
    • MR2139106
    • REN, J. and ZHANG, X. (2005). Schilder theorem for the Brownian motion on the diffeomorphism group of the circle. J. Funct. Anal. 224 107-133. MR2139106
    • (2005) J. Funct. Anal , vol.224 , pp. 107-133
    • REN, J.1    ZHANG, X.2
  • 24
    • 24644487849 scopus 로고    scopus 로고
    • Freidlin-Wentzell's large deviations for homeomorphism flows of non-Lipschitz SDEs
    • MR2166732
    • REN, J. and ZHANG, X. (2005). Freidlin-Wentzell's large deviations for homeomorphism flows of non-Lipschitz SDEs. Bull. Sci. Math. 129 643-655. MR2166732
    • (2005) Bull. Sci. Math , vol.129 , pp. 643-655
    • REN, J.1    ZHANG, X.2
  • 25
    • 0001835257 scopus 로고
    • Large deviations for a reaction-diffusion equation with non-Gaussian perturbations
    • MR1143433
    • SOWERS, R. B. (1992). Large deviations for a reaction-diffusion equation with non-Gaussian perturbations. Ann. Probab. 20 504-537. MR1143433
    • (1992) Ann. Probab , vol.20 , pp. 504-537
    • SOWERS, R.B.1
  • 26
    • 33749241702 scopus 로고    scopus 로고
    • Large deviations for the two dimensional NavierStokes equations with multiplicative noise
    • MR2269220
    • SRITHARAN, S.S. and SUNDAR, P. (2006). Large deviations for the two dimensional NavierStokes equations with multiplicative noise. Stochastic Process. Appl. 116 1636-1659. MR2269220
    • (2006) Stochastic Process. Appl , vol.116 , pp. 1636-1659
    • SRITHARAN, S.S.1    SUNDAR, P.2
  • 27
    • 52049122884 scopus 로고    scopus 로고
    • Reductions and deviations for stochastic differential equations under fast dynamical boundary conditions
    • Preprint
    • WANG, W. and DUAN, J. Reductions and deviations for stochastic differential equations under fast dynamical boundary conditions. Preprint.
    • WANG, W.1    DUAN, J.2
  • 28
    • 52049092579 scopus 로고    scopus 로고
    • WALSH, J. B. (1986). An introduction to stochastic partial differential equations. École d'Été de Probabilités de Saint Flour XIV - 1984. Lecture Notes in Math. 1180 265-439. Springer, Berlin. MR0876085
    • WALSH, J. B. (1986). An introduction to stochastic partial differential equations. École d'Été de Probabilités de Saint Flour XIV - 1984. Lecture Notes in Math. 1180 265-439. Springer, Berlin. MR0876085
  • 29
    • 0030181789 scopus 로고    scopus 로고
    • Large deviations for diffusion processes in duals of nuclear spaces
    • MR1389351
    • XIONG, J. (1996). Large deviations for diffusion processes in duals of nuclear spaces. Appl. Math. Optim. 34 1-27. MR1389351
    • (1996) Appl. Math. Optim , vol.34 , pp. 1-27
    • XIONG, J.1
  • 30
    • 52049105937 scopus 로고    scopus 로고
    • ZABCZYK, J. (.1988). On large deviations for stochastic evolution equations. Stochastic Systems and Optimization (Warsaw, 1988). Lecture Notes in Control and Inform. Sci. 136 240-253. Springer, Berlin. MR1180783
    • ZABCZYK, J. (.1988). On large deviations for stochastic evolution equations. Stochastic Systems and Optimization (Warsaw, 1988). Lecture Notes in Control and Inform. Sci. 136 240-253. Springer, Berlin. MR1180783


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.