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References
-
Adams, R.A. Sobolev Spaces. Pure and Applied Mathematics, Vol. 65,
Academic Press, New York-London, 1975. Math Review
link
- Carmona, R. and Nualart, D. Random nonlinear wave equations:
propagation of singularities. Annals Probab. 16 (1988), 730-751. Math Review
link
- Carmona, R. and Nualart, D. Random nonlinear wave equations: smoothness
of the solutions. Probab. Theory Related Fields 79 (1988), 469--508.
Math
Review link
- Da Prato, G. and Zabczyk, J. Stochastic Equations in Infinite
Dimensions. Encyclopedia of mathematics and its applications 44.
Cambridge University Press, Cambridge, New York, 1992. Math Review
link
- Dalang, R.C. Extending the martingale measure stochastic integral with
applications to spatially homogeneous s.p.d.e's. Electron. J. Probab. 4
(1999), 29pp. Math
Review link
- Dalang, R.C. and Frangos, N.E. The stochastic wave equation in two
spatial dimensions. Ann. Probab. 26-1 (1998), 187-212. Math Review
link
- Karczewska, A. and Zabczyk, J. Stochastic PDEs with function-valued
solutions. In: Infinite dimensional stochastic analysis (Amsterdam,
1999), Royal Neth. Acad. Arts Sci. 52, Amsterdam (2000), 197-216. Math
Review link
- Krylov, N.V. and Rozovskii, B.L. Stochastic evolution systems. J.
Soviet Math. 16 (1981), 1233-1276. Math Review number not
available.
- Krylov, N.V. and Rozovskii, B.L. Stochastic partial differential
equations and diffusion processes. Russian Math. Surveys 37 (1982),
81-105. Math Review
link
- Léveque, O. Hyperbolic stochastic partial differential equations
driven by boundary noises. Ph.D. thesis, no.2452, Ecole Polytechnique
Fédérale de Lausanne, Switzerland (2001). Math
Review number not available.
- Millet, A. and Sanz-Solé, M. A stochastic wave equation in two
space dimension: Smoothness of the law. Annals of Probab. 27 (1999),
803-844. Math
Review link
- Mueller, C. Long time existence for the wave equation with a noise
term. Ann. Probab. 25-1 (1997), 133-152. Math Review
link
- Oberguggenberger, M. and Russo, F. White noise driven stochastic
partial differential equations: triviality and non-triviality. In:
Nonlinear Theory of Generalized Functions (M. Grosser, G. Hormann, M.
Kunzinger & M. Oberguggenberger, eds), Chapman & Hall/CRC
Research Notes
in Mathematics Series, CRC Press (1999), 315-333. Math Review link - Oberguggenberger, M. and Russo, F. Nonlinear stochastic wave equations.
Integral Transform. Spec. Funct. 6 (1998), 71-83. Math Review
link
- Pardoux, E. Sur des équations aux dérivées
partielles stochastiques monotones. C. R. Acad. Sci. Paris Sér.
A-B 275 (1972), A101-A103. Math Review
link
- Pardoux, E. Equations aux dérivées partielles
stochastiques de type monotone. Séminaire sur les Equations aux
Dérivées Partielles (1974--1975), III, Exp. No. 2 (1975),
p.10. Math
Review link
- Pardoux, E. Characterization of the density of the conditional law in
the filtering of a diffusion with boundary. In: Recent developments in
statistics (Proc. European Meeting Statisticians, Grenoble, 1976).
North Holland, Amsterdam (1977), 559-565. Math Review
link
- Peszat, S. The Cauchy problem for a nonlinear stochastic wave equation
in any dimension. J. Evol. Equ. 2 (2002), 383-394. Math Review
number not available.
- Peszat, S. and Zabczyk, J. Stochastic evolution equations with a
spatially homogeneous Wiener process. Stoch. Proc. Appl. 72 (1997),
187-204. Math Review
link
- Peszat, S. and Zabczyk, J. Nonlinear stochastic wave and heat
equations. Probab. Theory Related Fields 116 (2000), 421-443. Math
Review link
- Sanz-Solé, M. and Sarra, M. Path properties of a class of
Gaussian processes with applications to spde's. In: Stochastic
processes, physics and geometry: new interplays, I (Leipzig, 1999).
(Gestesy, F., Holden, H., Jost, J., Paycha, S., Rockner, M. and
Scarlatti, S., eds). CMS Conf. Proc. 28, Amer. Math. Soc., Providence,
RI (2000), 303-316. Math
Review link
- Schwartz, L. Théorie des distributions. Hermann, Paris (1966).
Math Review
link
- Stein, E.M. Singular Integrals and Differentiability Properties of
Functions. Princeton University Press (1970). Math Review
link
- Walsh, J.B. An introduction to stochastic partial differential
equations, Ecole d'Eté de Prob. de St. Flour XIV, 1984, Lect.
Notes in Math 1180, Springer-Verlag (1986). Math Review
link

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