Browse > Article
http://dx.doi.org/10.14317/jami.2013.491

UNIFORM Lp-CONTINUITY OF THE SOLUTION OF STOCHASTIC DIFFERENTIAL EQUATIONS  

Kim, Young-Ho (Department of Mathematics, Changwon National University)
Publication Information
Journal of applied mathematics & informatics / v.31, no.3_4, 2013 , pp. 491-498 More about this Journal
Abstract
This note is concerned with the uniform $L^p$-continuity of solution for the stochastic differential equations under Lipschitz condition and linear growth condition. Furthermore, uniform $L^p$-continuity of the solution for the stochastic functional differential equation is given.
Keywords
It$\hat{o}$'s formula; Lipschitz condition; Weakened linear growth condition; p-th moment;
Citations & Related Records
Times Cited By KSCI : 2  (Citation Analysis)
연도 인용수 순위
1 X. Mao, Y. Shen, and C. Yuan, Almost surely asymptotic stability of neutral stochastic differential delay equations with Markovian switching, Stochastic process. Appl., 118 (2008) 1385-1406.   DOI   ScienceOn
2 Y. Ren, S. Lu and N. Xia, Remarks on the existence and uniqueness of the solution to stochastic functional differential equations with infinite delay, J. Comput. Appl. Math. 220 (2008) 364-372.   DOI   ScienceOn
3 Y. Ren and N. Xia, Existence, uniqueness and stability of the solutions to neutral stochastic functional differential equations with infinite delay, Appl. Math. Comput. 210 (2009) 72-79.   DOI   ScienceOn
4 Y. Ren and N. Xia, A note on the existence and uniqueness of the solution to neutral stochastic functional differential equations with infinite delay, Appl. Math. Comput. 214 (2009) 457-461.   DOI   ScienceOn
5 A. Tari and S. Shahmorad, Numerical solution of a class of two-dimensional nonlinear Volterra integral equations of the first kind, J. Appl. Math. and Informatics, 30 (2012) 463-475.   과학기술학회마을   DOI
6 F. Wei and K. Wang, The existence and uniqueness of the solution for stochastic functional differential equations with infinite delay, J. Math. Anal. Appl. 331 (2007) 516-531.   DOI   ScienceOn
7 Y.J. Cho, S.S. Dragomir, Y.-H. Kim: A note on the existence and uniqueness of the solutions to SFDEs. J. Inequal. Appl. 126 (2012) 1-16.
8 D. Henderson and P. Plaschko, Stochastic Differential Equations in Science and Engineering, World Scientific Publishing Co. (2006).
9 T.E. Govindan, Stability of mild solution of stochastic evolution equations with variable delay, Stochastic Anal. Appl. 21 (2003) 1059-1077.   DOI   ScienceOn
10 N. Halidias, Remarks and corrections on "An existence theorem for stochastic functional differential equations with dealys under weak assumptions, Statistics and Probability Letters 78, 2008" by N. Halidias and Y. Ren, Stochastics and Probability Letters 79 (2009) 2220-2222.   DOI   ScienceOn
11 Y.-H. Kim, An estimate on the solutions for stochastic functional differential equations, J. Appl. Math. and Informatics, 29 (2011) 1549-1556.   과학기술학회마을   DOI
12 V.B. Kolmanovskii, A. Myshkis, Applied Theory of Functional Differential Equations, Kluwer Academic Publishers, (1992).
13 K. Liu, Lyapunov functionals and asymptotic of stochastic delay evolution equations, Stochastics and Stochastic Rep. 63 (1998) 1-26.   DOI   ScienceOn
14 X. Li and X. Fu, Stability analysis of stochastic functional differential equations with infinite delay and its application to recurrent neural networks, J. Comput. Appl. Math. 234 (2010) 407-417.   DOI   ScienceOn
15 X. Mao, Stochastic Differential Equations and Applications, Horwood Publication Chichester, UK (2007).