Free Access
Issue
ESAIM: PS
Volume 10, September 2006
Page(s) 380 - 405
DOI https://doi.org/10.1051/ps:2006016
Published online 20 October 2006
  1. M. Abramowitz and I.A. Stegun, Handbook of mathematical functions. National Bureau of Standards (1964).
  2. R.A. Adams, Sobolev spaces. Academic Press, New York-London (1975).
  3. E. Alòs, J.A. León and D. Nualart, Stochastic heat equation with random coefficients. Probab. Theory Related Fields 115 (1999) 41–94. [CrossRef] [MathSciNet]
  4. R.C. Dalang and N.E. Frangos, The stochastic wave equation in two spatial dimensions. Ann. Probab. 26 (1998) 187–212. [CrossRef] [MathSciNet]
  5. R.C. Dalang, Extending the martingale measure stochastic integral with applications to spatially homogeneous s.p.d.e.'s. Electron. J. Probab. 4 (1999) 1–29. [CrossRef] [MathSciNet]
  6. G. Da Prato and J. Zabczyk, Stochastic Equations in Infinite Dimensions, 2nd Edition. Cambridge University Press (1998).
  7. W.F. Donoghue, Distributions and Fourier transforms. Academic Press, New York (1969).
  8. S.D. Eidelman and N.V. Zhitarashu, Parabolic Boundary Value Problems. Birkhäuser Verlag, Basel (1998).
  9. A. Friedman, Partial differential equations of parabolic type. Prentice-Hall, Inc., Englewood Cliffs, N.J. (1964).
  10. I.M. Gel'fand and N.Ya. Vilenkin, Generalized functions. Vol. 4: Applications of harmonic analysis. Academic Press, New York (1964).
  11. M.A Krasnoselskii, E.I. Pustylnik, P.E. Sobolevski and P.P. Zabrejko, Integral operators in spaces of summable functions. Noordhoff International Publishing, Leyden (1976).
  12. A.A. Kirillov and A.D. Gvishiani, Theorems and problems in functional analysis. Springer-Verlag, New York-Berlin (1982).
  13. N.V. Krylov and B.L. Rozovsky, Stochastic evolution systems. Russian Math. Surveys 37 (1982) 81–105. [CrossRef]
  14. N.V. Krylov, On Lp-theory of stochastic partial differential equations in the whole space. SIAM J. Math. Anal. 27 (1996) 313–340. [CrossRef] [MathSciNet]
  15. N.V. Krylov, An analytic approach to SPDEs, in Stochastic partial differential equations: six perspectives, Math. Surveys Monogr. 64, American Mathematical Society, Providence (1999) 185–242.
  16. N.V. Krylov and V. Lototsky, A Sobolev space theory of SPDEs with constant coefficients on a half line. SIAM J. Math. Anal. 30 (1998) 298–325. [CrossRef]
  17. O.A. Ladyženskaja, V.A. Solonnikov and N.N. Ural'ceva, Linear and Quasilinear Equations of Parabolic Type. Translations of Mathematical Monographs 23, American Mathematical Society (1968).
  18. O. Lévêque, Hyperbolic stochastic partial differential equations driven by boundary noises. Thèse 2452, Lausanne, EPFL (2001).
  19. R. Mikulevicius, On the Cauchy problem for parabolic SPDEs in Hölder classes. Ann. Probab. 28 (2000) 74–103. [CrossRef] [MathSciNet]
  20. E. Pardoux, Stochastic partial differential equations and filtering of diffusion processes. Stochastics 3 (1979) 127–167. [MathSciNet]
  21. B.L. Rozovsky, Stochastic evolution equations. Linear theory and applications to non-linear filtering. Kluwer (1990).
  22. L. Schwartz, Théorie des distributions. Hermann, Paris (1966).
  23. M. Sanz-Solé and M. Sarrà, Path properties of a class of Gaussian processes with applications to spde's. Canadian Mathematical Society Conference Proceedings 28 (2000) 303–316.
  24. M. Sanz-Solé and M. Sarrà, Hölder Continuity for the stochastic heat equation with spatially correlated noise, in Progress in Probability 52, Birkhäuser Verlag (2002) 259–268.
  25. M. Sanz-Solé and P.-A. Vuillermot, Equivalence and Hölder-Sobolev regularity of solutions for a class of non-autonomous stochastic partial differential equations. Ann. Inst. H. Poincaré Probab. Statist. 39 (2003) 703–742. [CrossRef] [MathSciNet]
  26. N. Shimakura, Partial differential operators of elliptic type. American Mathematical Society, Providence (1992).
  27. H. Triebel, Theory of function spaces. II. Monographs in Mathematics 84, Birkhäuser Verlag, Basel (1992).
  28. J.B. Walsh, An Introduction to Stochastic Partial Differential Equations, in École d'été de Probabilités de Saint-Flour XIV (1984). Lect. Notes Math. 1180 (1986) 265–439. [CrossRef]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.