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DOI QR Code

BOUNDEDNESS AND CONTINUITY OF SOLUTIONS FOR STOCHASTIC DIFFERENTIAL INCLUSIONS ON INFINITE DIMENSIONAL SPACE

  • Yun, Yong-Sik (DEPARTMENT OF MATHEMATICS COLLEGE OF NATURAL SCIENCES CHEJU NATIONAL UNIVERSITY) ;
  • Ryu, Sang-Uk (DEPARTMENT OF MATHEMATICS COLLEGE OF NATURAL SCIENCES CHEJU NATIONAL UNIVERSITY)
  • Published : 2007.11.30

Abstract

For the stochastic differential inclusion on infinite dimensional space of the form $dX_t{\in}\sigma(X_t)dW_t+b(X_t)dt$, where ${\sigma}$, b are set-valued maps, W is an infinite dimensional Hilbert space valued Q-Wiener process, we prove the boundedness and continuity of solutions under the assumption that ${\sigma}$ and b are closed convex set-valued satisfying the Lipschitz property using approximation.

Keywords

stochastic differential inclusion;Wiener process

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