메뉴 건너뛰기




Volumn 67, Issue 1, 2013, Pages 123-161

Large deviations and importance sampling for systems of slow-fast motion

Author keywords

Homogenization; Importance sampling; Large deviations; Monte Carlo; Multiscale; Slow fast motion

Indexed keywords

HOMOGENIZATION; LARGE DEVIATIONS; MONTE CARLO; MULTISCALES; SLOW-FAST MOTION;

EID: 84872687177     PISSN: 00954616     EISSN: 14320606     Source Type: Journal    
DOI: 10.1007/s00245-012-9183-z     Document Type: Article
Times cited : (67)

References (35)
  • 1
    • 0036338482 scopus 로고    scopus 로고
    • Viscosity solutions methods for singular perturbations in deterministic and stochastic control
    • 1882729 10.1137/S0363012900366741 1017.49028
    • Alvarez, O., Bardi, M.: Viscosity solutions methods for singular perturbations in deterministic and stochastic control. SIAM J. Control Optim. 40(4), 1159-1188 (2001)
    • (2001) SIAM J. Control Optim. , vol.40 , Issue.4 , pp. 1159-1188
    • Alvarez, O.1    Bardi, M.2
  • 2
    • 0009909157 scopus 로고    scopus 로고
    • On ergodic stochastic control
    • 1662180 10.1080/03605309808821413 1126.93434
    • Arisawa, M., Lions, P.-L.: On ergodic stochastic control. Commun. Partial Differ. Equ. 23, 2187-2217 (1998)
    • (1998) Commun. Partial Differ. Equ. , vol.23 , pp. 2187-2217
    • Arisawa, M.1    Lions, P.-L.2
  • 3
    • 0042894343 scopus 로고
    • Large deviations for diffusions processes with homogenization and applications
    • 1106273 10.1214/aop/1176990438 0735.60026
    • Baldi, P.: Large deviations for diffusions processes with homogenization and applications. Ann. Probab. 19(2), 509-524 (1991)
    • (1991) Ann. Probab. , vol.19 , Issue.2 , pp. 509-524
    • Baldi, P.1
  • 7
    • 36949037739 scopus 로고    scopus 로고
    • Averaging of singularly perturbed controlled stochastic differential equations
    • 2352935 10.1007/s00245-007-0893-6 1139.93022
    • Borkar, V., Gaitsgory, V.: Averaging of singularly perturbed controlled stochastic differential equations. Appl. Math. Optim. 56(2), 169-209 (2007)
    • (2007) Appl. Math. Optim. , vol.56 , Issue.2 , pp. 169-209
    • Borkar, V.1    Gaitsgory, V.2
  • 8
    • 0032237648 scopus 로고    scopus 로고
    • A variational representation for certain functionals of Brownian motion
    • 1675051 10.1214/aop/1022855876 0936.60059
    • Boué, M., Dupuis, P.: A variational representation for certain functionals of Brownian motion. Ann. Probab. 26(4), 1641-1659 (1998)
    • (1998) Ann. Probab. , vol.26 , Issue.4 , pp. 1641-1659
    • Boué, M.1    Dupuis, P.2
  • 9
    • 11244262559 scopus 로고    scopus 로고
    • Limit theorem for controlled backward SDEs and homogenization of Hamilton-Jacobi-Bellman equations
    • 2101380 10.1007/s00245-004-0805-3 1109.60055
    • Buckdahn, R., Ichihara, N.: Limit theorem for controlled backward SDEs and homogenization of Hamilton-Jacobi-Bellman equations. Appl. Math. Optim. 51, 1-33 (2005)
    • (2005) Appl. Math. Optim. , vol.51 , pp. 1-33
    • Buckdahn, R.1    Ichihara, N.2
  • 10
    • 67650727363 scopus 로고    scopus 로고
    • Rates of convergence in periodic homogenization of fully nonlinear uniformly elliptic PDEs
    • 2507330 10.1088/0951-7715/22/6/011 1172.35318
    • Camilli, F., Marchi, C.: Rates of convergence in periodic homogenization of fully nonlinear uniformly elliptic PDEs. Nonlinearity 22, 1481-1498 (2009)
    • (2009) Nonlinearity , vol.22 , pp. 1481-1498
    • Camilli, F.1    Marchi, C.2
  • 12
    • 84858713706 scopus 로고    scopus 로고
    • Large deviations for multiscale problems via weak convergence methods
    • 2914778 10.1016/j.spa.2011.12.006 1247.60034
    • Dupuis, P., Spiliopoulos, K.: Large deviations for multiscale problems via weak convergence methods. Stoch. Process. Appl. 122, 1947-1987 (2012)
    • (2012) Stoch. Process. Appl. , vol.122 , pp. 1947-1987
    • Dupuis, P.1    Spiliopoulos, K.2
  • 15
    • 36749081774 scopus 로고    scopus 로고
    • Subsolutions of an Isaacs equation and efficient schemes for importance sampling
    • 2348245 10.1287/moor.1070.0266 05279751
    • Dupuis, P., Wang, H.: Subsolutions of an Isaacs equation and efficient schemes for importance sampling. Math. Oper. Res. 32(3), 723-757 (2007)
    • (2007) Math. Oper. Res. , vol.32 , Issue.3 , pp. 723-757
    • Dupuis, P.1    Wang, H.2
  • 17
    • 84974059058 scopus 로고
    • Periodic homogenization of certain fully nonlinear partial differential equations
    • 10.1017/S0308210500032121 0796.35011
    • Evans, L.: Periodic homogenization of certain fully nonlinear partial differential equations. Proc. R. Soc. Edinb., Sect. A 120, 245-265 (1992)
    • (1992) Proc. R. Soc. Edinb., Sect. A , vol.120 , pp. 245-265
    • Evans, L.1
  • 18
    • 84872682316 scopus 로고    scopus 로고
    • Small-time asymptotics for fast mean-reverting stochastic volatility models
    • 10.1214/11-AAP801 06083943
    • Feng, J., Fouque, J.-P., Kumar, R.: Small-time asymptotics for fast mean-reverting stochastic volatility models. Ann. Appl. Probab. 22(4), 1541-1575 (2012)
    • (2012) Ann. Appl. Probab. , vol.22 , Issue.4 , pp. 1541-1575
    • Feng, J.1    Fouque, J.-P.2    Kumar, R.3
  • 19
    • 0042636802 scopus 로고    scopus 로고
    • A comparison of homogenization and large deviations, with applications to wavefront propagation
    • 1695068 10.1016/S0304-4149(99)00003-4 0996.60035
    • Freidlin, M., Sowers, R.: A comparison of homogenization and large deviations, with applications to wavefront propagation. Stoch. Process. Appl. 82(1), 23-52 (1999)
    • (1999) Stoch. Process. Appl. , vol.82 , Issue.1 , pp. 23-52
    • Freidlin, M.1    Sowers, R.2
  • 20
    • 19944362518 scopus 로고    scopus 로고
    • Computing the effective Hamiltonian using a variational approach
    • 2114376 10.1137/S0363012902417620
    • Gomes D, D., Oberman, A.: Computing the effective Hamiltonian using a variational approach. SIAM J. Control Optim. 43, 792-812 (2004)
    • (2004) SIAM J. Control Optim. , vol.43 , pp. 792-812
    • Gomes, D.D.1    Oberman, A.2
  • 21
    • 84970902023 scopus 로고    scopus 로고
    • Simultaneous effects of homogenization and vanishing viscosity in fully nonlinear elliptic equations
    • 1996294 10.1619/fesi.46.63 1151.35351
    • Horie, K., Ishii, H.: Simultaneous effects of homogenization and vanishing viscosity in fully nonlinear elliptic equations. Funkc. Ekvacioj 46(1), 63-88 (2003)
    • (2003) Funkc. Ekvacioj , vol.46 , Issue.1 , pp. 63-88
    • Horie, K.1    Ishii, H.2
  • 22
    • 33644939007 scopus 로고    scopus 로고
    • On the structure of solutions of ergodic type Bellman equation related to risk-sensitive control
    • 2206349 10.1214/009117905000000431 1092.60030
    • Kaise, H., Sheu, S.J.: On the structure of solutions of ergodic type Bellman equation related to risk-sensitive control. Ann. Probab. 34(1), 284-320 (2006)
    • (2006) Ann. Probab. , vol.34 , Issue.1 , pp. 284-320
    • Kaise, H.1    Sheu, S.J.2
  • 23
    • 58149105938 scopus 로고    scopus 로고
    • Ergodic type Bellman equations of first order with quadratic Hamiltonian
    • 2465707 10.1007/s00245-008-9043-z 1166.49028
    • Kaise, H., Sheu, S.J.: Ergodic type Bellman equations of first order with quadratic Hamiltonian. Appl. Math. Optim. 59(1), 37-73 (2009)
    • (2009) Appl. Math. Optim. , vol.59 , Issue.1 , pp. 37-73
    • Kaise, H.1    Sheu, S.J.2
  • 25
    • 78049529258 scopus 로고    scopus 로고
    • Large deviations for two-time-scale diffusions with delays
    • 2727337 10.1007/s00245-010-9104-y
    • Kushner, H.J.: Large deviations for two-time-scale diffusions with delays. Appl. Math. Optim. 62(3), 295-322 (2009)
    • (2009) Appl. Math. Optim. , vol.62 , Issue.3 , pp. 295-322
    • Kushner, H.J.1
  • 26
    • 36849120663 scopus 로고
    • On the self-diffusion of ions in a polyelectrolyte solution
    • 10.1063/1.1732899
    • Lifson, S., Jackson, J.L.: On the self-diffusion of ions in a polyelectrolyte solution. J. Chem. Phys. 36, 2410-2414 (1962)
    • (1962) J. Chem. Phys. , vol.36 , pp. 2410-2414
    • Lifson, S.1    Jackson, J.L.2
  • 27
    • 24944549463 scopus 로고    scopus 로고
    • Homogenization of degenerate second-order PDE in periodic and almost periodic environments and applications
    • 2171996 10.1016/j.anihpc.2004.10.009 1135.35092
    • Lions, P.-L., Souganidis, P.E.: Homogenization of degenerate second-order PDE in periodic and almost periodic environments and applications. Ann. Inst. Henri Poincaré, Anal. Non Linéaire 22(5), 667-677 (2005)
    • (2005) Ann. Inst. Henri Poincaré, Anal. Non Linéaire , vol.22 , Issue.5 , pp. 667-677
    • Lions, P.-L.1    Souganidis, P.E.2
  • 28
    • 0012862641 scopus 로고    scopus 로고
    • Large deviations for two scaled diffusions
    • 10.1007/s004400050058
    • Lipster, R.: Large deviations for two scaled diffusions. Probab. Theory Relat. Fields 106(1), 71-104 (1996)
    • (1996) Probab. Theory Relat. Fields , vol.106 , Issue.1 , pp. 71-104
    • Lipster, R.1
  • 29
    • 60749128340 scopus 로고    scopus 로고
    • Noise-induced transport in a rough racket potential
    • 074703 10.1063/1.3076934
    • Mondal, D., Ghosh, P.K., Ray, D.S.: Noise-induced transport in a rough racket potential. J. Chem. Phys. 130, 074703 (2009)
    • (2009) J. Chem. Phys. , vol.130
    • Mondal, D.1    Ghosh, P.K.2    Ray, D.S.3
  • 30
    • 0038336352 scopus 로고    scopus 로고
    • On Poisson equation and diffusion approximation 2
    • 1988467 10.1214/aop/1055425774 1054.60064
    • Pardoux, E., Veretennikov, A.Yu.: On Poisson equation and diffusion approximation 2. Ann. Probab. 31(3), 1166-1192 (2003)
    • (2003) Ann. Probab. , vol.31 , Issue.3 , pp. 1166-1192
    • Pardoux, E.1    Veretennikov, A.Yu.2
  • 32
    • 0001081429 scopus 로고
    • Kinetics of protein folding: The dynamics of globally connected rough energy landscapes with biases
    • 10.1063/1.467855
    • Saven, J.G., Wang, J., Wolynes, P.G.: Kinetics of protein folding: the dynamics of globally connected rough energy landscapes with biases. J. Chem. Phys. 101(12), 11037-11043 (1994)
    • (1994) J. Chem. Phys. , vol.101 , Issue.12 , pp. 11037-11043
    • Saven, J.G.1    Wang, J.2    Wolynes, P.G.3
  • 33
    • 0033243135 scopus 로고    scopus 로고
    • On large deviations in the averaging principle for SDEs with a "full dependence", correction, arXiv:math/0502098v1 [math.PR]
    • Veretennikov, A.Yu.: On large deviations in the averaging principle for SDEs with a "full dependence", correction, arXiv:math/0502098v1 [math.PR] (2005). Initial article in Ann. Probab. 27(1), 284-296 (1999)
    • (1999) Initial Article in Ann. Probab. , vol.27 , Issue.1 , pp. 284-296
    • Veretennikov, A.Yu.1
  • 34
    • 0041914537 scopus 로고    scopus 로고
    • On large deviations for SDEs with small diffusion and averaging
    • 1775227 10.1016/S0304-4149(00)00013-2 1045.60065
    • Veretennikov, A.Yu.: On large deviations for SDEs with small diffusion and averaging. Stoch. Process. Appl. 89(1), 69-79 (2000)
    • (2000) Stoch. Process. Appl. , vol.89 , Issue.1 , pp. 69-79
    • Veretennikov, A.Yu.1
  • 35
    • 0024121530 scopus 로고
    • Diffusion in a rough potential
    • 934660 10.1073/pnas.85.7.2029
    • Zwanzig, R.: Diffusion in a rough potential. Proc. Natl. Acad. Sci. USA 85, 2029-2030 (1988)
    • (1988) Proc. Natl. Acad. Sci. USA , vol.85 , pp. 2029-2030
    • Zwanzig, R.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.