메뉴 건너뛰기




Volumn 1905, Issue , 2007, Pages 1-152

A concise course on stochastic partial differential equations

Author keywords

[No Author keywords available]

Indexed keywords


EID: 34547290416     PISSN: 00758434     EISSN: None     Source Type: Book Series    
DOI: 10.1007/978-3-540-70781-3     Document Type: Review
Times cited : (654)

References (30)
  • 2
    • 0000364933 scopus 로고
    • Stochastic differential equations in infinite dimensions: Solutions via Dirichlet forms
    • MR MR1113223 92k:60123
    • S. Albeverio and M. Röckner, Stochastic differential equations in infinite dimensions: solutions via Dirichlet forms, Probab. Theory Related Fields 89 (1991), no. 3, 347-386. MR MR1113223 (92k:60123)
    • (1991) Probab. Theory Related Fields , vol.89 , Issue.3 , pp. 347-386
    • Albeverio, S.1    Röckner, M.2
  • 3
    • 0002293879 scopus 로고
    • The porous medium equation
    • Nonlinear diffusion problems (Montecatini Terme, Springer, Berlin, MR MR877986 88a:35130
    • D. G. Aronson, The porous medium equation, Nonlinear diffusion problems (Montecatini Terme, 1985), Lecture Notes in Math., vol. 1224, Springer, Berlin, 1986, pp. 1-46. MR MR877986 (88a:35130)
    • (1985) Lecture Notes in Math , vol.1224 , pp. 1-46
    • Aronson, D.G.1
  • 6
    • 0003954462 scopus 로고
    • John Wiley & Sons Inc, New York, MR MR0058896 15,445b
    • J. L. Doob, Stochastic processes, John Wiley & Sons Inc., New York, 1953. MR MR0058896 (15,445b)
    • (1953) Stochastic processes
    • Doob, J.L.1
  • 8
    • 31744446404 scopus 로고    scopus 로고
    • Strong solutions of stochastic generalized porous media equations: Existence, uniqueness, and ergodicity
    • MR MR2209754
    • G. Da Prato, M. Röckner, B. L. Rozowskii and F. Y. Wang, Strong solutions of stochastic generalized porous media equations: existence, uniqueness, and ergodicity, Comm. Partial Differential Equations 31 (2006), nos 1-3, 277-291. MR MR2209754
    • (2006) Comm. Partial Differential Equations , vol.31 , Issue.1-3 , pp. 277-291
    • Da Prato, G.1    Röckner, M.2    Rozowskii, B.L.3    Wang, F.Y.4
  • 11
    • 85009412751 scopus 로고    scopus 로고
    • K. Frieler and C. Knoche, Solutions of stochastic differential equations in infinite dimensional Hilbert spaces and their dependence on initial data, Diploma Thesis, Bielefeld University, BiBoS-Preprint E02-04-083, 2001.
    • K. Frieler and C. Knoche, Solutions of stochastic differential equations in infinite dimensional Hilbert spaces and their dependence on initial data, Diploma Thesis, Bielefeld University, BiBoS-Preprint E02-04-083, 2001.
  • 12
    • 0002473786 scopus 로고
    • On stochastic equations with respect to semimartingales. I
    • MR MR587426 82j:60104
    • I. Gyöngy and N. V. Krylov, On stochastic equations with respect to semimartingales. I, Stochastics 4 (1980/81), no. 1, 1-21. MR MR587426 (82j:60104)
    • (1980) Stochastics , vol.4 , Issue.1 , pp. 1-21
    • Gyöngy, I.1    Krylov, N.V.2
  • 13
    • 0010028630 scopus 로고
    • On stochastics equations with respect to semimartingales. II. Itô formula in Banach spaces
    • MR MR665398 84m:60070a
    • _, On stochastics equations with respect to semimartingales. II. Itô formula in Banach spaces, Stochastics 6 (1981/82), nos 3-4, 153-173. MR MR665398 (84m:60070a)
    • (1981) Stochastics , vol.6 , Issue.3-4 , pp. 153-173
    • Gyöngy, I.1    Krylov, N.V.2
  • 14
    • 0003549965 scopus 로고
    • second ed, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences, Springer-Verlag, Berlin, MR MR737190 86c:35035
    • D. Gilbarg and N. S. Trudinger, Elliptic, partial differential equations of second order, second ed., Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 224, Springer-Verlag, Berlin, 1983. MR MR737190 (86c:35035)
    • (1983) Elliptic, partial differential equations of second order , vol.224
    • Gilbarg, D.1    Trudinger, N.S.2
  • 15
    • 0020199364 scopus 로고
    • On stochastic equations with respect to semimartingales. III
    • MR MR674448 84m:60070b
    • I. Gyöngy, On stochastic equations with respect to semimartingales. III, Stochastics 7 (1982), no. 4, 231-254. MR MR674448 (84m:60070b)
    • (1982) Stochastics , vol.7 , Issue.4 , pp. 231-254
    • Gyöngy, I.1
  • 17
    • 85009402513 scopus 로고    scopus 로고
    • N. V. Krylov and B. L. Rozowskiǐ, Stochastic evolution equations, Current problems in mathematics, 14 (Russian), Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Informatsii, Moscow, 1979, pp. 71-147, 256. MR MR570795 (81m:60116)
    • N. V. Krylov and B. L. Rozowskiǐ, Stochastic evolution equations, Current problems in mathematics, Vol. 14 (Russian), Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Informatsii, Moscow, 1979, pp. 71-147, 256. MR MR570795 (81m:60116)
  • 18
    • 85009343368 scopus 로고    scopus 로고
    • N. V. Krylov, On Kolmogorov's equations for finite-dimensional diffusions, Stochastic PDE's and Kolmogorov equations in infinite dimensions (Cetraro, 1998), Lecture Notes in Math., 1715, Springer, Berlin, 1999, pp. 1-63. MR MR1731794 (2000k:60155)
    • N. V. Krylov, On Kolmogorov's equations for finite-dimensional diffusions, Stochastic PDE's and Kolmogorov equations in infinite dimensions (Cetraro, 1998), Lecture Notes in Math., vol. 1715, Springer, Berlin, 1999, pp. 1-63. MR MR1731794 (2000k:60155)
  • 19
    • 0003242243 scopus 로고
    • Brownian motion and stochastic calculus
    • Springer-Verlag, New York, MR MR917065 89c:60096
    • I. Karatzas and S. E. Shreve, Brownian motion and stochastic calculus, Graduate Texts in Mathematics, vol. 113, Springer-Verlag, New York, 1988. MR MR917065 (89c:60096)
    • (1988) Graduate Texts in Mathematics , vol.113
    • Karatzas, I.1    Shreve, S.E.2
  • 22
    • 0005432757 scopus 로고
    • Sur des équations aux dérivées partielles stochastiques monotones
    • MR MR0312572 47 #1129
    • E. Pardoux, Sur des équations aux dérivées partielles stochastiques monotones, C. R. Acad. Sci. Paris Sér. A-B 275 (1972), A101-A103. MR MR0312572 (47 #1129)
    • (1972) C. R. Acad. Sci. Paris Sér. A-B , vol.275
    • Pardoux, E.1
  • 23
    • 10644237319 scopus 로고
    • Séminaire sur les Équations aux Dérivées Partielles, III, Exp, Collège de France, Paris, MR MR0651582 (58 #31406) 1975
    • _, Equations aux dérivées partielles stochastiques de type monotone, Séminaire sur les Équations aux Dérivées Partielles (1974-1975), III, Exp. No. 2, Collège de France, Paris, 1975, p. 10. MR MR0651582 (58 #31406)
    • (1974) Equations aux dérivées partielles stochastiques de type monotone , Issue.2 , pp. 10
    • Pardoux, E.1
  • 27
    • 0000659593 scopus 로고
    • An introduction to stochastic partial differential equations
    • École d'été de probabilités de Saint-Flour, XIV, Springer, Berlin, MR MR876085 88a:60114
    • J. B. Walsh, An introduction to stochastic partial differential equations, École d'été de probabilités de Saint-Flour, XIV - 1984, Lecture Notes in Math., vol. 1180, Springer, Berlin, 1986, pp. 265-439. MR MR876085 (88a:60114)
    • (1984) Lecture Notes in Math , vol.1180 , pp. 265-439
    • Walsh, J.B.1
  • 29
    • 0005353894 scopus 로고    scopus 로고
    • Parabolic equations on Hilbert spaces
    • Stochastic PDEs and Kolmogorov Equations in Infinite Dimensions, ed, Springer Verlag
    • J. Zabczyk, Parabolic equations on Hilbert spaces, Stochastic PDEs and Kolmogorov Equations in Infinite Dimensions (Giuseppe Da Prato, ed.), Lecture Notes in Mathematics, Springer Verlag, 1998, pp. 117-213.
    • (1998) Lecture Notes in Mathematics , pp. 117-213
    • Zabczyk, J.1
  • 30
    • 85009381412 scopus 로고    scopus 로고
    • E. Zeidler, Nonlinear functional analysis and its applications. II/B, Springer-Verlag, New York, 1990, Nonlinear monotone operators, Translated from the German by the author and Leo F. Boron. MR MR1033498 (91b:47002)
    • E. Zeidler, Nonlinear functional analysis and its applications. II/B, Springer-Verlag, New York, 1990, Nonlinear monotone operators, Translated from the German by the author and Leo F. Boron. MR MR1033498 (91b:47002)


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.