Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

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
Download PDF
⟨ Previous Next ⟩

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

References

  1. N. U. Ahmed, Nonlinear stochastic differential inclusions on Banach space, Stochastic Anal. Appl. 12 (1994), no. 1, 1-10 https://doi.org/10.1080/07362999408809334
  2. J. P. Aubin and G. D. Prato, The viability theorem for stochastic differential inclusions, Stochastic Anal. Appl. 16 (1998), no. 1, 1-15 https://doi.org/10.1080/07362999808809512
  3. A. A. Levakov, Asymptotic behavior of solutions of stochastic differential inclusions, Differ. Uravn. 34 (1998), no. 2, 204-210
  4. G. D. Prato and J. Zabczyk, Stochastic equations in infinite dimensions, Encyclopedia of Mathematics and its Applications, 44. Cambridge University Press, Cambridge, 1992
  5. B. Truong-Van and X. D. H. Truong, Existence results for viability problem associated to nonconvex stochastic differentiable inclusions, Stochastic Anal. Appl. 17 (1999), no. 4, 667-685 https://doi.org/10.1080/07362999908809628
  6. B. Truong-Van and X. D. H. Truong, Existence of viable solutions for a nonconvex stochastic differential inclusion, Discuss. Math. Differential Incl. 17 (1997), no. 1-2, 107-131
  7. Y. S. Yun, On the estimation of approximate solution for SDI, Korean Ann. Math. 20 (2003), 63-69
  8. Y. S. Yun and I. Shigekawa, The existence of solutions for stochastic differential inclu- sion, Far East J. Math. Sci. (FJMS) 7 (2002), no. 2, 205-212