• Title/Summary/Keyword: weakened linear growth condition

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AN EXISTENCE AND UNIQUENESS THEOREM OF STOCHASTIC DIFFERENTIAL EQUATIONS AND THE PROPERTIES OF THEIR SOLUTION

  • BAE, MUN-JIN;PARK, CHAN-HO;KIM, YOUNG-HO
    • Journal of applied mathematics & informatics
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    • v.37 no.5_6
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    • pp.491-506
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    • 2019
  • In this paper, we show the existence and uniqueness of solution to stochastic differential equations under weakened $H{\ddot{o}}lder$ condition and a weakened linear growth condition. Furthermore, the properties of their solutions investigated and estimate for the error between Picard iterations $x_n(t)$ and the unique solution x(t) of SDEs.

A NOTE ON THE APPROXIMATE SOLUTIONS TO STOCHASTIC DIFFERENTIAL DELAY EQUATION

  • KIM, YOUNG-HO;PARK, CHAN-HO;BAE, MUN-JIN
    • Journal of applied mathematics & informatics
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    • v.34 no.5_6
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    • pp.421-434
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    • 2016
  • The main aim of this paper is to discuss the difference between the Euler-Maruyama's approximate solutions and the accurate solution to stochastic differential delay equation. To make the theory more understandable, we impose the non-uniform Lipschitz condition and weakened linear growth condition. Furthermore, we give the pth moment continuous of the approximate solution for the delay equation.

UNIFORM Lp-CONTINUITY OF THE SOLUTION OF STOCHASTIC DIFFERENTIAL EQUATIONS

  • Kim, Young-Ho
    • Journal of applied mathematics & informatics
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    • v.31 no.3_4
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    • pp.491-498
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    • 2013
  • 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.

AN EXISTENCE OF THE SOLUTION TO NEUTRAL STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS UNDER SPECIAL CONDITIONS

  • KIM, YOUNG-HO
    • Journal of applied mathematics & informatics
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    • v.37 no.1_2
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    • pp.53-63
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    • 2019
  • In this paper, we show the existence of solution of the neutral stochastic functional differential equations under non-Lipschitz condition, a weakened linear growth condition and a contractive condition. Furthermore, in order to obtain the existence of solution to the equation we used the Picard sequence.

AN ESTIMATE OF THE SOLUTIONS FOR STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS

  • Kim, Young-Ho
    • Journal of applied mathematics & informatics
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    • v.29 no.5_6
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    • pp.1549-1556
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    • 2011
  • 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.