본문 바로가기
KERD
논문KCI 등재

THE DIFFERENCE BETWEEN THE APPROXIMATE AND THE ACCURATE SOLUTION TO STOCHASTIC DIFFERENTIAL DELAY EQUATION

김영호
장전수학회 (Jangjeon Mathematical Society)|2015.04|Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집) (Proceedings of the Jangjeon Mathematical Society)|제18권 제2호|pp. 165-175|DOI 10.17777/pjms.2015.18.2.004

1

조회

0

다운로드

0

인용

0

참고문헌

키워드

Caratheodory approximationDoob's martingale inequalityEuler-Maruyama approximationHölder's inequalityStochastic differential delay equation
주제분류수학

초록

The main aim of this paper is to discuss the difference between the approximate solution and the accurate solution to stochastic differential delay equation. To make the theory more understandable, we use the Caratheodory's and Euler-Maruyama's approximate solutions and impose the non-uniform Lips- chitz condition and non-linear growth condition.

Abstract

The main aim of this paper is to discuss the difference between the approximate solution and the accurate solution to stochastic differential delay equation. To make the theory more understandable, we use the Caratheodory's and Euler-Maruyama's approximate solutions and impose the non-uniform Lips- chitz condition and non-linear growth condition.

참고문헌 (12)

  1. Y. J. Cho, "A note on the existence and uniqueness of the solutions to SFDEs", J. Inequal. Appl., 126, pp.1~16 (2012)
  2. T.E. Govindan, "Stability of mild solution of stochastic evolution equations with variable delay", Stochastic Anal. Appl., 21, pp.1059~1077 (2003)
  3. N. Halidias, "Remarks and corrections on "An existence theorem for stochastic functional dif-ferential equations with delays under weak assumptions, Statistics and Probability Letters 78, 2008", Statistics and Probability Letters, 79, pp.2220~2222 (2009)
  4. Y. -H. Kim, "A note on the solutions of Neutral SFDEs with in nite delay", J. Inequal. Appl., 181, pp.1~12 (2013)
  5. Y. -H. Kim, "On the pth moment estimates for the solution of stochastic differential equations", J. Inequal. Appl., 29 (2014)
  6. X. Li, "Stability analysis of stochastic functional differential equations with in nite delay and its application to recurrent neural networks", J. Comput. Appl. Math, 234, pp.407~417 (2010)
  7. X. Mao, "Stochastic Differential Equations and Applications" (2007), Horwood Publication Chichester
  8. J. Randjelovic, "On the pth moment exponential stability criteria of neutral stochastic functional differential equations", J. Math. Anal. Appl, 326, pp.266~280 (2007)
  9. Y. Ren, "Remarks on the existence and uniqueness of the solutions to stochastic functional differential equations with in nite delay", J. Comput. Appl. Math., 220, pp.364~372 (2008)
  10. Y. Ren, "Existence, uniqueness and stability of the solutions to neutral stochastic functional differential equations with infinite delay", Appl. Math. Comput., 210, pp.72~79 (2009)
  11. F. Wei, "The existence and uniqueness of the solution for stochastic functional differential equations with infinite delay", J. Math. Anal. Appl., 331, pp.516~531 (2007)
  12. F. Wei, "Existence, uniqueness and stability of the solution to neutral stochastic functional differential equations with infinite delay under non-Lipschitz conditions", Advances in Difference Equations, 2013, pp.151~ (2013)

관련 논문AI추천

The uniqueness of the solutions for stochastic differential equations김영호장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2011 · 제14권 제4호Moment estimate and existence for the solution of neutral stochastic functional differential equationHuabin Chen, Qunjia Wan대한수학회 · 대한수학회지2022 · 제59권 제2호A Taylor approximation of the solutions of neutral stochastic differential equations with constant delay under polynomial conditionsDusan D. Djordjevic, Marija Milosevic, Miljana Jovanovic대한수학회 · 대한수학회지2025 · 제62권 제5호On the existence and uniqueness of solution of stochastic differential system driven by G-Brownian motionEL-HACENE CHALABI, HACENE BOUTABIA장전수학회 · Advanced Studies in Contemporary Mathematics2019 · 제29권 제4호A note on exponential almost sure stability of stochastic differential equationDichuan Yang, Qingshuo Song, Xuerong Mao대한수학회 · 대한수학회보2014 · 제51권 제1호On the general decay stability of stochastic differential equations with unbounded delayBaojian Yin, Xuejing Meng대한수학회 · 대한수학회지2012 · 제49권 제3호

이 간행물의 다른 논문 (11건)

A QUALITATIVE RESULT CONCERNING QUASIREPRESENTATIONS OF COMPACT GROUPSA. I. Shternpp. 139-143EXAMPLES OF NON-DIFFERENTIABILITY POINTS OF RIESZ-NÁGY-TAKÁCS FUNCTION백인수pp. 145-151THE ANALYSIS OF STUDENTS’ SURVEY FOR THE CHANGE OF SECONDARY SCHOOL TEACHERS’ TEACHING BEHAVIOR BASED ON SELF-REFLECTIONJ. Kwonpp. 153-163A symmetric identity on the q-Genocchi polynomials of higher-order under third dihedral group D3M. Acikgoz, S. Araci, E. Agyüzpp. 177-187Identities Involving Generalized Harmonic NumbersD. S. Kim, Y. Jeongpp. 189-199
원문 보기