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 Electronic Journal of Probability > Vol. 6 (2001) > Paper 12 open journal systems 


A Note on Krylov's Lp-Theory for Systems of SPDEs

R. Mikulevicius, Vilnius University
B. Rozovskii, University of Southern California


Abstract
We extend Krylov's L_p-solvability theory to the Cauchy problem for systems of parabolic stochastic partial differential equations. Some additional integrability and regularity properties are also presented.


Full text: PDF

Pages: 1-35

Published on: March 14, 2001


Bibliography
  1. N. V. Krylov, On L_p-theory of stochastic partial differential equations, SIAM J. Math. Anal. 27 (1996), 313--340. Math Review link
  2. N. V. Krylov, An analytic approach to SPDEs, In: Stochastic Partial Differential Equations: Six Perspectives, AMS Mathematical Surveys and Monographs 64 (1999), 185--242. Math Review link
  3. Z. Brzezniak, Stochastic partial differential equations in M-type 2 Banach spaces, Potential Anal. 4 (1995), 1--45. Math Review link
  4. A. L. Neihardt, Stochastic integrals in 2-uniformly smooth Banach spaces, Ph. D. Thesis, University of Wisconsin, (1978). Math. Review number not available.
  5. R. Mikulevicius, B.L. Rozovskii, Martingale problems for SPDEs, In: Stochastic Partial Differential Equations: Six Perspectives (Editors: R. Carmona and B. L. Rozovskii), AMS, Mathematical Surveys and Monographs 64 (1999), 243--325. Math Review link
  6. R. Mikulevicius, B. L. Rozovskii, On Equations of Stochastic Fluid Mechanics In: Stochastics in Finite and Infinite Dimensions: In Honor of Gopinath Kallianpur (Editors: T. Hida, R. Karandikar, H. Kunita, B. Rajput, S. Watanabe and J. Xiong ), Birkhauser, (2001), 285--302. Math. Review number not available.
  7. R. Mikulevicius, B. L. Rozovskii, Stochastic Navier-Stokes Equations. Propagation of Chaos and Statistical Moments, In: A. Bensoussan Festschrift, IOS Press, Amsterdam, (2001), (to appear). Math. Review number not available.
  8. H. Triebel, Theory of Function Spaces, Birkhauser, Basel, Boston, Stutgart, (1983). Math Review link
  9. J. B. Walsh, An introduction to stochastic partial differential equations, In: Ecole d'Ete' de Probabilite's de Saint-Flour XIV (1984), 265--439, Lecture Notes in Math. 1180 , Springer-Verlag, NewYork, (1986). Math Review link
  10. J. Bergh, J. Loefstroem, Interpolation Spaces, Springer-Verlag, Berlin, (1976). Math Review link
  11. E. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton University Press, Princeton, (1970). Math Review link
  12. M. Yor, Sur les integrales stochastiques a valeurs dans un espace de Banach, Ann. Inst. Henri Poincare, 10(1) (1974), 31--36 Math Review link
















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Electronic Journal of Probability. ISSN: 1083-6489