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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 저널정보
- 한국전산응용수학회 Journal of applied mathematics & informatics Journal of applied mathematics & informatics 제29권 제5호
- 발행연도
- 2011.1
- 수록면
- 1,549 - 1,556 (8page)
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In this paper, we give an estimate on the difference between $x^n(t)$ and x(t) and it clearly shows that one can use the Picard iteration procedure to the approximate solutions to stochastic functional differential equations with infinite delay at phase space BC(($-{\infty}$, 0] : $R^d$) which denotes the family of bounded continuous $R^d$-valued functions ${\varphi}$ defined on ($-{\infty}$, 0] with norm ${\parallel}{\varphi}{\parallel}={\sup}_{-{\infty}<{\theta}{\leq}0}{\mid}{\varphi}({\theta}){\mid}$ under non-Lipschitz condition being considered as a special case and a weakened linear growth condition.
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참고문헌 (11)
참고문헌 신청
R. Bellman / 1943 / The stability of solutions of linear differential equations / Duke Math. J 10:643~647
I. Bihari / 1956 / A generalization of a lemma of Bellman and its application to uniqueness problem of differential equations / Acta Math. Acad. Sci. Hungar 7:71~94
Y. El. Boukfaoui / 2002 / Remarks on the existence and approximation for semilinear stochastic differential in Hilbert spaces / Stochastic Anal. Appl 20:495~518
T.E. Govindan / 2003 / Stability of mild solution of stochastic evolution equations with variable delay / Stochastic Anal. Appl 21:1059~1077
N. Halidias / 2009 / Remarks and corrections on "An esistence 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 79:2220~2222
I. Bihari / 1956 / A generalization of a lemma of Bellman and its application to uniqueness problem of differential equations / Acta Math. Acad. Sci. Hungar 7:71~94
Y. El. Boukfaoui / 2002 / Remarks on the existence and approximation for semilinear stochastic differential in Hilbert spaces / Stochastic Anal. Appl 20:495~518
T.E. Govindan / 2003 / Stability of mild solution of stochastic evolution equations with variable delay / Stochastic Anal. Appl 21:1059~1077
N. Halidias / 2009 / Remarks and corrections on "An esistence 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 79:2220~2222
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