Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

THE CLOSED PROPERTY OF SET OF SOLUTIONS FOR STOCHASTIC DIFFERENTIAL INCLUSIONS

  • YUN, YONG-SIK (Department of Mathematics College of Natural Sciences Cheju National University)
  • Published : 2005.01.01
Download PDF
⟨ Previous Next ⟩

Abstract

We consider the stochastic differential inclusion of the form $dX_t{\in}{\sigma}(t, X_t)dB_t+b(t, X_t)dt$, where ${\sigma}$, b are set-valued maps, B is a standard Brownian motion. We prove that the set of solutions is closed.

Keywords

References

  1. N. U. Ahmed, Nonlinear stochastic difierential inclusions on Banach space, Stochastic Anal. Appl. 12 (1994), no. 1, 1-10 https://doi.org/10.1080/07362999408809334
  2. J. P. Aubin and A. Cellina, Differential Inclusions, Springer-Verlag, Berlin, 1984
  3. 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
  4. N. Ikeda and S. Watanabe, Stochastic differential equations and diffusion pros- esses; North Holland-Kodansha, Tokyo, 1981
  5. A. A. Levakov, Asymptotic behavior of solutions of stochastic differential inclu- sions, Differ. Uravn. 34 (1998), no. 2, 204-210
  6. B. Truong-Van and X. D. H. Truong, Existence results for viability problem associated to nonconvex stochastic differential inclusions, Stochastic Anal. Appl. 17 (1999), no. 4, 667-685 https://doi.org/10.1080/07362999908809628
  7. Y. S. Yun and I. Shigekawa, The existence of solutions for stochastic differential inclusion, Far East J. Math. Sci. 7 (2002), no. 2, 205-212
  8. Y. S. Yun, The boundedness of solutions for stochastic differential inclusions, Bull. Korean Math. Soc. 40 (2003), no. 1, 159-165 https://doi.org/10.4134/BKMS.2003.40.1.159
  9. Y. S. Yun, On the estimation of approximate solution for SDI, Korean Ann. Math. 20 (2003), 63-69