대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제18권4호
  • /
  • Pages.713-723
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  • 2003
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  • 1225-1763(pISSN)
  • /
  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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LIMIT OF SOLUTIONS OF A SPDE DRIVEN BY MARTINGALE MEASURE WITH REFLECTION

  • Cho, Nhan-Sook (Department of general science and Department of computer science and information Hansung University) ;
  • Kwon, Young-Mee (Department of general science and Department of computer science and information Hansung University)
  • 발행 : 2003.10.01
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초록

We study a limit problem of reflected solutions of parabolic stochastic partial differential equations driven by martingale measures. The existence of solutions is found in an extension of the work with respect to white noise by Donati-Martin and Pardoux [4]. We show that if a certain sequence of driving martingale measures converges, the corresponding solutions also converge in the Skorohod topology.

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참고문헌

  1. Convergence of probability measures P.Billingsley
  2. Stochastic Process Appl v.59 Weak convergence of stochastic integrals driven by martingale measure N.Cho https://doi.org/10.1016/0304-4149(95)00031-2
  3. Stochastics and Stochastics reports v.67 On the intersection local time of super Brownian motion N.Cho https://doi.org/10.1080/17442509908834210
  4. Probab. Theory Relat. Fields v.95 White noise driven SPDEs with reflection C.Donald-Martin;E.Pardoux https://doi.org/10.1007/BF01197335
  5. Markov processes : Characterization and convergence E.Ethier;T.Kurtz
  6. Electronic J. of Probab. v.5 SPDE in $L_q$ spaces N.V.Krylov https://doi.org/10.1214/ECP.v5-1013
  7. Probab. Theory Relat. Fields v.90 Long time existence for the heat equation with a noise C.Mueller https://doi.org/10.1007/BF01192141
  8. Probab. Theory Relat. Fields v.93 White noise driven quasilinear SPDEs with reflection D.Nualart;E.Pardoux https://doi.org/10.1007/BF01195389
  9. Stochastics v.3 Stochastic partial differential equations and filtering of diffusion processes E.Pardoux
  10. Springer Lect. notes in mathematics v.1180 An introduction to stochastic partial differential equations J.Walsh https://doi.org/10.1007/BFb0074920