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Volumn 27, Issue 2, 1999, Pages 615-652

The stable manifold theorem for stochastic differential equations

Author keywords

(perfect) cocycle; Asymptotic invariance; Hyperbolic stationary trajectory; Local characteristics; Local stable unstable manifolds; Lyapuncv exponents; Spatial semimartingale; Stochastic differential equation (SDE); Stochastic flow

Indexed keywords


EID: 0033455085     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/aop/1022677380     Document Type: Article
Times cited : (85)

References (28)
  • 2
    • 0030097426 scopus 로고    scopus 로고
    • Stratonovich calculus with spatial parameters and anticipative problems in multiplicative ergodic theory
    • ARNOLD, L. and IMKELLER, P. (1996). Stratonovich calculus with spatial parameters and anticipative problems in multiplicative ergodic theory. Stochastic Process. Appl. 62 19-54.
    • (1996) Stochastic Process. Appl. , vol.62 , pp. 19-54
    • Arnold, L.1    Imkeller, P.2
  • 3
    • 21844488246 scopus 로고
    • Perfect cocycles through stochastic differential equations
    • ARNOLD, L. and SCHEUTZOW, M. K. R. (1995). Perfect cocycles through stochastic differential equations. Probab. Theory Related Fields 101 65-88.
    • (1995) Probab. Theory Related Fields , vol.101 , pp. 65-88
    • Arnold, L.1    Scheutzow, M.K.R.2
  • 4
    • 0001846760 scopus 로고
    • Stability and equilibrium properties of stochastic flows of diffeomorphisms
    • (M. Pinsky and V. Wihstutz, eds.) Birkhäuser, Boston
    • BAXENDALE, P. H. (1992). Stability and equilibrium properties of stochastic flows of diffeomorphisms. In Diffusion Processes and Related Problems in Analysis 2 (M. Pinsky and V. Wihstutz, eds.) 3-35. Birkhäuser, Boston.
    • (1992) Diffusion Processes and Related Problems in Analysis , vol.2 , pp. 3-35
    • Baxendale, P.H.1
  • 5
    • 0011607426 scopus 로고
    • A stochastic version of center manifold theory
    • BOXLER, P. (1989). A stochastic version of center manifold theory. Probab. Theory Related Fields 83 509-545.
    • (1989) Probab. Theory Related Fields , vol.83 , pp. 509-545
    • Boxler, P.1
  • 6
    • 0007837893 scopus 로고
    • Flows of stochastic dynamical systems: Ergodic theory
    • CARVERHILL, A. (1985). Flows of stochastic dynamical systems: ergodic theory. Stochastics 14 273-317.
    • (1985) Stochastics , vol.14 , pp. 273-317
    • Carverhill, A.1
  • 7
    • 0000062381 scopus 로고
    • Markov measures for random dynamical systems
    • CRAUEL, H. (1991). Markov measures for random dynamical systems. Stochastics Stochastic Rep. 37 153-173.
    • (1991) Stochastics Stochastic Rep. , vol.37 , pp. 153-173
    • Crauel, H.1
  • 8
    • 0033243148 scopus 로고    scopus 로고
    • On the spatial asymptotic behavior of stochastic flows in Euclidean space
    • To appear
    • IMKELLER, P. and SCHEUTZOW, M. K. R. (1999). On the spatial asymptotic behavior of stochastic flows in Euclidean space. Ann. Probab. To appear.
    • (1999) Ann. Probab.
    • Imkeller, P.1    Scheutzow, M.K.R.2
  • 11
    • 0001405311 scopus 로고
    • Équilibre statistique pour les produits de difféomorphisries aléatoires indépendants
    • LE JAN, Y. (1987). Équilibre statistique pour les produits de difféomorphisries aléatoires indépendants. Ann. Inst. H. Poincaré Probab. Statist. 23 111-120.
    • (1987) Ann. Inst. H. Poincaré Probab. Statist. , vol.23 , pp. 111-120
    • Le Jan, Y.1
  • 13
    • 0000535958 scopus 로고
    • Large deviations for a class of anticipating stochastic differential equations
    • MILLET, A., NUALART, D. and SANZ, M. (1992). Large deviations for a class of anticipating stochastic differential equations. Ann. Probab. 20 1902-1931.
    • (1992) Ann. Probab. , vol.20 , pp. 1902-1931
    • Millet, A.1    Nualart, D.2    Sanz, M.3
  • 14
    • 0003238077 scopus 로고
    • Lyapunov exponents and stochastic flows of linear and affine hereditary systems
    • (M. Pinsky and V. Wihstutz, eds.) Birkhäuser, Boston
    • MOHAMMED, S.-E. A. (1992). Lyapunov exponents and stochastic flows of linear and affine hereditary systems. In Diffusion Processes and Related Problems in Analysis 2 (M. Pinsky and V. Wihstutz, eds.) 141-169. Birkhäuser, Boston.
    • (1992) Diffusion Processes and Related Problems in Analysis , vol.2 , pp. 141-169
    • Mohammed, S.-E.A.1
  • 15
    • 0009304630 scopus 로고
    • The Lyapunov spectrum and stable manifolds for stochastic linear delay equations
    • MOHAMMED, S.-E. A. (1990). The Lyapunov spectrum and stable manifolds for stochastic linear delay equations. Stochastics Stochastic Rep. 29 89-131.
    • (1990) Stochastics Stochastic Rep. , vol.29 , pp. 89-131
    • Mohammed, S.-E.A.1
  • 16
    • 21844507454 scopus 로고    scopus 로고
    • Lyapunov exponents of linear stochastic functional differential equations driven by semimartingales I: The multiplicative ergodic theory
    • MOHAMMED, S.-E. A. and SCHEUTZOW, M. K. R. (1996). Lyapunov exponents of linear stochastic functional differential equations driven by semimartingales I: the multiplicative ergodic theory. Ann. Inst. H. Poincaré, Probab. Statist. 32 69-105.
    • (1996) Ann. Inst. H. Poincaré, Probab. Statist. , vol.32 , pp. 69-105
    • Mohammed, S.-E.A.1    Scheutzow, M.K.R.2
  • 17
    • 0032359438 scopus 로고    scopus 로고
    • Spatial estimates for stochastic flows in Euclidean space
    • MOHAMMED, S.-E. A. and SCHEUTZOW, M. K. R. (1998). Spatial estimates for stochastic flows in Euclidean space. Ann. Probab. 26 56-77.
    • (1998) Ann. Probab. , vol.26 , pp. 56-77
    • Mohammed, S.-E.A.1    Scheutzow, M.K.R.2
  • 19
    • 0001626619 scopus 로고
    • Stochastic calculus with anticipating integrands, Analysis on Wiener space and anticipating stochastic calculus
    • NUALART, D. and PARDOUX, E. (1988). Stochastic calculus with anticipating integrands, Analysis on Wiener space and anticipating stochastic calculus. Probab. Theory Related Fields 78 535-581.
    • (1988) Probab. Theory Related Fields , vol.78 , pp. 535-581
    • Nualart, D.1    Pardoux, E.2
  • 20
    • 0002383320 scopus 로고
    • A generalized Itô-Ventzell formula. Application to a class of anticipating stochastic differential equations
    • OCONE, D. and PARDOUX, E. (1989). A generalized Itô-Ventzell formula. Application to a class of anticipating stochastic differential equations. Ann. Inst. H. Poincaré Probab. Statist. 25 39-71.
    • (1989) Ann. Inst. H. Poincaré Probab. Statist. , vol.25 , pp. 39-71
    • Ocone, D.1    Pardoux, E.2
  • 21
    • 0038434713 scopus 로고
    • A multiplicative ergodic theorem. Lyapunov characteristic numbers for dynamical systems
    • OSELEDEC, V. I. (1968). A multiplicative ergodic theorem. Lyapunov characteristic numbers for dynamical systems. Trudy Moskov. Mat. Obšč. 19 179-210. (English trans. Trans. Moscow Math. Soc. 19 197-221.)
    • (1968) Trudy Moskov. Mat. Obšč. , vol.19 , pp. 179-210
    • Oseledec, V.I.1
  • 22
    • 85033944082 scopus 로고    scopus 로고
    • OSELEDEC, V. I. (1968). A multiplicative ergodic theorem. Lyapunov characteristic numbers for dynamical systems. Trudy Moskov. Mat. Obšč. 19 179-210. (English trans. Trans. Moscow Math. Soc. 19 197-221.)
    • Trans. Moscow Math. Soc. , vol.19 , pp. 197-221
  • 25
    • 51649166261 scopus 로고
    • Ergodic theory of differentiable dynamical systems
    • RUELLE, D. (1979). Ergodic theory of differentiable dynamical systems. Publ. Math. Inst. Hautes Etud. Sci. 275-306.
    • (1979) Publ. Math. Inst. Hautes Etud. Sci. , pp. 275-306
    • Ruelle, D.1
  • 26
    • 0000320029 scopus 로고
    • Characteristic exponents and invariant manifolds in Hilbert space
    • RUELLE, D. (1982). Characteristic exponents and invariant manifolds in Hilbert space. Ann. of Math. 115 243-290.
    • (1982) Ann. of Math. , vol.115 , pp. 243-290
    • Ruelle, D.1
  • 27
    • 0040570354 scopus 로고    scopus 로고
    • On the perfection of crude cocycles
    • SCHEUTZOW, M. K. R. (1996). On the perfection of crude cocycles. Random Comput. Dynam. 4 235-255.
    • (1996) Random Comput. Dynam. , vol.4 , pp. 235-255
    • Scheutzow, M.K.R.1
  • 28
    • 0011618959 scopus 로고
    • Linearization of random dynamical systems
    • (U. Kirchgraber and H. O. Walther, eds.) Springer, New York
    • WANNER, T. (1995). Linearization of random dynamical systems. In Dynamics Reported 4 (U. Kirchgraber and H. O. Walther, eds.) 203-269. Springer, New York.
    • (1995) Dynamics Reported , vol.4 , pp. 203-269
    • Wanner, T.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.