Browse > Article
http://dx.doi.org/10.4134/CKMS.2005.20.1.135

THE CLOSED PROPERTY OF SET OF SOLUTIONS FOR STOCHASTIC DIFFERENTIAL INCLUSIONS  

YUN, YONG-SIK (Department of Mathematics College of Natural Sciences Cheju National University)
Publication Information
Communications of the Korean Mathematical Society / v.20, no.1, 2005 , pp. 135-144 More about this Journal
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
stochastic differential inclusion; Brownian motion;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
1 N. Ikeda and S. Watanabe, Stochastic differential equations and diffusion pros- esses; North Holland-Kodansha, Tokyo, 1981
2 A. A. Levakov, Asymptotic behavior of solutions of stochastic differential inclu- sions, Differ. Uravn. 34 (1998), no. 2, 204-210
3 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   DOI   ScienceOn
4 N. U. Ahmed, Nonlinear stochastic difierential inclusions on Banach space, Stochastic Anal. Appl. 12 (1994), no. 1, 1-10   DOI
5 J. P. Aubin and A. Cellina, Differential Inclusions, Springer-Verlag, Berlin, 1984
6 J. P. Aubin and G. D. Prato, The viability theorem for stochastic differential inclusions, Stochastic Anal. Appl. 16 (1998), no. 1, 1-15   DOI   ScienceOn
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   DOI   ScienceOn
9 Y. S. Yun, On the estimation of approximate solution for SDI, Korean Ann. Math. 20 (2003), 63-69