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Volumn 9, Issue 4, 1996, Pages 863-901

The law of the solution to a nonlinear hyperbolic SPDE

Author keywords

Hyperbolic SPDE's; Large deviations; Malliavin calculus; Strong and weak solution

Indexed keywords


EID: 21444439436     PISSN: 08949840     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02214255     Document Type: Article
Times cited : (25)

References (22)
  • 1
    • 0002053916 scopus 로고
    • Grandes déviations et applications; École d'été de Probabilités de Saint-Flour VIII
    • Springer Verlag
    • Azencott, R. (1980). Grandes déviations et applications; École d'été de Probabilités de Saint-Flour VIII, Springer Verlag, Lect. Notes. Math. 779, 1-176.
    • (1980) Lect. Notes. Math. , vol.779 , pp. 1-176
    • Azencott, R.1
  • 3
    • 0006148134 scopus 로고
    • Sur une équation différentielle stochastique
    • Cairoli, R. (1972). Sur une équation différentielle stochastique. C.R. Acad. Sci. Paris 274, 1739-1742.
    • (1972) C.R. Acad. Sci. Paris , vol.274 , pp. 1739-1742
    • Cairoli, R.1
  • 4
    • 0009095592 scopus 로고
    • Stochastic integrals in the plane
    • Cairoli, R., and Walsh, J. B. (1975). Stochastic integrals in the plane. Acta Math. 134, 111-183.
    • (1975) Acta Math. , vol.134 , pp. 111-183
    • Cairoli, R.1    Walsh, J.B.2
  • 5
    • 0011040823 scopus 로고
    • Estimations des grandes déviations pour les processus de diffusion à paramètre multidimensionnel
    • Séminaire de Probabilités XX. Springer Verlag
    • Doss, H., and Dozzi, M. (1986). Estimations des grandes déviations pour les processus de diffusion à paramètre multidimensionnel. Séminaire de Probabilités XX. Springer Verlag, Lect. Notes Math. 1204, 68-79.
    • (1986) Lect. Notes Math. , vol.1204 , pp. 68-79
    • Doss, H.1    Dozzi, M.2
  • 6
    • 0000497486 scopus 로고
    • Petites perturbations des systèmes dynamiques avec reflexion
    • Springer Verlag. Séminaire de Probabilités XVII.
    • Doss, H., and Priouret, P. (1983). Petites perturbations des systèmes dynamiques avec reflexion. Springer Verlag. Séminaire de Probabilités XVII. Lect. Notes Math. 986, 353-370.
    • (1983) Lect. Notes Math. , vol.986 , pp. 353-370
    • Doss, H.1    Priouret, P.2
  • 7
    • 27544434989 scopus 로고
    • Hyperbolic stochastic differential equations: Absolute continuity of the law of the solution at a fixed point
    • to appear
    • Farré, M. (1995). Hyperbolic stochastic differential equations: absolute continuity of the law of the solution at a fixed point. Appl. Math. Optim. (to appear).
    • (1995) Appl. Math. Optim.
    • Farré, M.1
  • 8
    • 38249003033 scopus 로고
    • Nonlinear stochastic integral equation in the plane
    • Farré, M., and Nualart, D. (1993). Nonlinear stochastic integral equation in the plane. Stoch. Proc. Appl. 46, 219-239.
    • (1993) Stoch. Proc. Appl. , vol.46 , pp. 219-239
    • Farré, M.1    Nualart, D.2
  • 9
    • 0041381665 scopus 로고
    • Thèse de Doctorat d'État. Sci. Math. de Paris Sud
    • 2. Thèse de Doctorat d'État. Sci. Math. de Paris Sud.
    • (1980) 2
    • Guyon, X.1    Prum, B.2
  • 12
    • 0000923387 scopus 로고
    • Estimation de Varadhan pour des diffusions à deux paramètres
    • Léandre, R., and Russo, F. (1990). Estimation de Varadhan pour des diffusions à deux paramètres. Prob. Th. Rel. Fields 84, 429-451.
    • (1990) Prob. Th. Rel. Fields , vol.84 , pp. 429-451
    • Léandre, R.1    Russo, F.2
  • 14
    • 0002684408 scopus 로고
    • Stochastic calculus of variations and hypoelliptic operators
    • John Wiley
    • Malliavin, P. (1978). Stochastic calculus of variations and hypoelliptic operators. Proc. Int'l. Conf. Stoch. Differ. Eqs. Kyoto 1976, pp. 195-263. John Wiley.
    • (1978) Proc. Int'l. Conf. Stoch. Differ. Eqs. Kyoto 1976 , pp. 195-263
    • Malliavin, P.1
  • 15
    • 0000535958 scopus 로고
    • Large deviations for a class of anticipating stochastic differential equations
    • Millet, A., Nualart, D., and Sanz-Solé, M. (1992). Large deviations for a class of anticipating stochastic differential equations. Ann. Prob. 20, 1902-1931.
    • (1992) Ann. Prob. , vol.20 , pp. 1902-1931
    • Millet, A.1    Nualart, D.2    Sanz-Solé, M.3
  • 16
    • 58149364016 scopus 로고
    • Twisted Sheets
    • Norris, J. R. (1995). Twisted Sheets. J. Funct. Analysis 132, 273-334.
    • (1995) J. Funct. Analysis , vol.132 , pp. 273-334
    • Norris, J.R.1
  • 17
    • 0001671126 scopus 로고
    • Malliavin calculus for two-parameter Wiener functionals
    • Nualart, D., and Sanz-Solé, M. (1985). Malliavin calculus for two-parameter Wiener functionals. Z. Wahrsch. Verw. Gebiete 70, 573-590.
    • (1985) Z. Wahrsch. Verw. Gebiete , vol.70 , pp. 573-590
    • Nualart, D.1    Sanz-Solé, M.2
  • 18
    • 38249006489 scopus 로고
    • Stochastic Differential Equtions on the plane: Smoothness of the solution
    • Nualart, D., and Sanz-Solé, M. (1989). Stochastic Differential Equtions on the plane: Smoothness of the solution. J. Multivariate Anal. 31, 1-29.
    • (1989) J. Multivariate Anal. , vol.31 , pp. 1-29
    • Nualart, D.1    Sanz-Solé, M.2
  • 19
    • 0001860369 scopus 로고
    • A nonlinear hyperbolic SPDE: Approximations and support
    • Etheridge, A. (ed.), Stochastic Partial Differential Equations Cambridge University Press
    • Rovira, C., and Sanz-Solé, M. (1995). A nonlinear hyperbolic SPDE: Approximations and support. In Etheridge, A. (ed.), Stochastic Partial Differential Equations pp. 241-261. London Mathematical Society Lecture Note Series 216. Cambridge University Press.
    • (1995) London Mathematical Society Lecture Note Series 216 , pp. 241-261
    • Rovira, C.1    Sanz-Solé, M.2
  • 20
    • 0001835257 scopus 로고
    • Large deviations for a reaction-diffusion equation with non-Gaussian perturbations
    • Sowers, R B. (1992). Large deviations for a reaction-diffusion equation with non-Gaussian perturbations. Ann. Prob. 20, 504-537.
    • (1992) Ann. Prob. , vol.20 , pp. 504-537
    • Sowers, R.B.1
  • 21
    • 0000216024 scopus 로고
    • Weak martingales and stochastic integrals in the plane
    • Wong E., and Zakai, M. (1974). Weak martingales and stochastic integrals in the plane. Ann. Prob. 4, 570-586.
    • (1974) Ann. Prob. , vol.4 , pp. 570-586
    • Wong, E.1    Zakai, M.2
  • 22
    • 84972514664 scopus 로고
    • Existence of strong solutions for stochastic differential equations in the plane
    • Yeh, H. (1981). Existence of strong solutions for stochastic differential equations in the plane. Pacific J. Math. 97, 217-297.
    • (1981) Pacific J. Math. , vol.97 , pp. 217-297
    • Yeh, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.