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Volumn 144, Issue 1-2, 2009, Pages 137-177

Averaging principle for a class of stochastic reaction-diffusion equations

Author keywords

Averaging principle; Invariant measures and ergodicity; Kolmogorov equations in Hilbert spaces; Stochastic reaction diffusion equations

Indexed keywords


EID: 60449117774     PISSN: 01788051     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00440-008-0144-z     Document Type: Article
Times cited : (208)

References (21)
  • 3
    • 0034383575 scopus 로고    scopus 로고
    • On stochastic behavior of perturbed Hamiltonian systems
    • M. Brin M.I. Freidlin 2000 On stochastic behavior of perturbed Hamiltonian systems Ergod. Theory Dyn. Syst. 20 55 76
    • (2000) Ergod. Theory Dyn. Syst. , vol.20 , pp. 55-76
    • Brin, M.1    Freidlin, M.I.2
  • 4
    • 0003196688 scopus 로고    scopus 로고
    • Second order PDE's in finite and infinite dimension. A probabilistic approach
    • Springer, Heidelberg
    • Cerrai, S.: Second order PDE's in finite and infinite dimension. A probabilistic approach. In: Lecture Notes in Mathematics, vol. 1762, x+330 pp. Springer, Heidelberg (2001)
    • (2001) Lecture Notes in Mathematics , vol.1762
    • Cerrai, S.1
  • 6
    • 0035532611 scopus 로고    scopus 로고
    • On stable oscillations and equilibrium induced by small noise
    • M.I. Freidlin 2001 On stable oscillations and equilibrium induced by small noise J. Stat. Phys. 103 283 300
    • (2001) J. Stat. Phys. , vol.103 , pp. 283-300
    • Freidlin, M.I.1
  • 8
    • 33748306215 scopus 로고    scopus 로고
    • Long-time behavior of weakly coupled oscillators
    • M.I. Freidlin A.D. Wentzell 2006 Long-time behavior of weakly coupled oscillators J. Stat. Phys. 123 1311 1337
    • (2006) J. Stat. Phys. , vol.123 , pp. 1311-1337
    • Freidlin, M.I.1    Wentzell, A.D.2
  • 9
    • 0040361064 scopus 로고    scopus 로고
    • Existence of strong solutions for Itô's stochastic equations via approximations
    • I. Gyöngy N.V. Krylov 1996 Existence of strong solutions for Itô's stochastic equations via approximations Probab. Theory Relat. Fields 103 143 158
    • (1996) Probab. Theory Relat. Fields , vol.103 , pp. 143-158
    • Gyöngy, I.1    Krylov, N.V.2
  • 10
    • 0000182826 scopus 로고
    • On the principle of averaging the Itô's stochastic differential equations (Russian)
    • R.Z. Khasminskii 1968 On the principle of averaging the Itô's stochastic differential equations (Russian) Kibernetika 4 260 279
    • (1968) Kibernetika , vol.4 , pp. 260-279
    • Khasminskii, R.Z.1
  • 11
    • 28444456514 scopus 로고    scopus 로고
    • Some recent advances in averaging
    • Cambridge University Press, Cambridge
    • Kifer, Y.: Some recent advances in averaging. In: Modern Dynamical Systems and Applications, pp. 385-403. Cambridge University Press, Cambridge (2004)
    • (2004) Modern Dynamical Systems and Applications , pp. 385-403
    • Kifer, Y.1
  • 12
    • 2942597464 scopus 로고    scopus 로고
    • Diffusion approximation for slow motion in fully coupled averaging
    • Y. Kifer 2004 Diffusion approximation for slow motion in fully coupled averaging Probab Theory Relat Fields 129 157 181
    • (2004) Probab Theory Relat Fields , vol.129 , pp. 157-181
    • Kifer, Y.1
  • 13
    • 2942629833 scopus 로고    scopus 로고
    • Averaging and climate models
    • Stochastic Climate Models (Chorin Birkhuser, Basel
    • Kifer, Y.: Averaging and climate models. In: Stochastic Climate Models (Chorin, 1999). Progress in Probability, vol. 49, pp. 171-188. Birkhuser, Basel (2001)
    • (1999) Progress in Probability , vol.49 , pp. 171-188
    • Kifer, Y.1
  • 14
    • 0347544115 scopus 로고    scopus 로고
    • Stochastic versions of Anosov's and Neistadt's theorems on averaging
    • Y. Kifer 2001 Stochastic versions of Anosov's and Neistadt's theorems on averaging Stochast. Dyn. 1 1 21
    • (2001) Stochast. Dyn. , vol.1 , pp. 1-21
    • Kifer, Y.1
  • 15
    • 41149100058 scopus 로고    scopus 로고
    • Khasminski-Whitman averaging for randonly perturbed KdV equations
    • in press
    • Kuksin, S.B., Piatnitski, A.L.: Khasminski-Whitman averaging for randonly perturbed KdV equations. J Math Pures Appl (2008, in press)
    • (2008) J Math Pures Appl
    • Kuksin, S.B.1    Piatnitski, A.L.2
  • 16
    • 0009379160 scopus 로고
    • An averaging principle for stochastic evolution equations. II
    • B. Maslowski J. Seidler I. Vrkoč 1991 An averaging principle for stochastic evolution equations. II Mathematica Bohemica 116 191 224
    • (1991) Mathematica Bohemica , vol.116 , pp. 191-224
    • Maslowski, B.1    Seidler, J.2    Vrkoč, I.3
  • 17
    • 0037993028 scopus 로고
    • Averaging in multyfrequency systems
    • A. Neishtadt 1976 Averaging in multyfrequency systems Sov. Phys. Doktagy 21 80 82
    • (1976) Sov. Phys. Doktagy , vol.21 , pp. 80-82
    • Neishtadt, A.1
  • 18
    • 0010398784 scopus 로고
    • Martingale approach to some limit theorems
    • Duke Univ. Duhram, N.C. Paper 6, ii+120 pp. Duke Univ. Math. Ser. Duke Univ. Duhram, N.C.
    • Papanicolaou, G.C., Stroock, D., Varadhan, S.R.S.: Martingale approach to some limit theorems. In: Papers from the Duke Turbolence Conference (Duke Univ. Duhram, N.C. 1976), Paper 6, ii+120 pp. Duke Univ. Math. Ser., vol. III. Duke Univ. Duhram, N.C. (1977)
    • (1976) Papers from the Duke Turbolence Conference , vol.3
    • Papanicolaou, G.C.1    Stroock, D.2    Varadhan, S.R.S.3
  • 19
    • 29744444403 scopus 로고
    • An averaging principle for stochastic evolution equations
    • J. Seidler I. Vrkoč 1990 An averaging principle for stochastic evolution equations Časopis Pěst. Mat. 115 240 263
    • (1990) Časopis Pěst. Mat. , vol.115 , pp. 240-263
    • Seidler, J.1    Vrkoč, I.2
  • 20
    • 2942695660 scopus 로고
    • On the averaging principle for systems of stochastic differential equation
    • A.Y. Veretennikov 1991 On the averaging principle for systems of stochastic differential equation Math. USSR-Sbornik 69 271 284
    • (1991) Math. USSR-Sbornik , vol.69 , pp. 271-284
    • Veretennikov, A.Y.1
  • 21
    • 0003003451 scopus 로고
    • Averaging in systems of ordinary differential equations
    • V.M. Volosov 1962 Averaging in systems of ordinary differential equations Russ. Math. Surv. 17 1 126
    • (1962) Russ. Math. Surv. , vol.17 , pp. 1-126
    • Volosov, V.M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.