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Section B

The improved stability analysis of the backward Euler method for neutral stochastic delay differential equations

Pages 1489-1494 | Received 26 Mar 2012, Accepted 02 Dec 2012, Published online: 07 Mar 2013

References

  • Li , Q. and Gan , S. 2011 . Almost sure exponential stability of numerical solutions for stochastic delay differential equations with jumps . J. Appl. Math. Comput. , 37 : 541 – 557 . (doi:10.1007/s12190-010-0449-9)
  • Mao , X. 2000 . Asymptotic properties of neutral stochastic differential delay equations . Stoch. Stoch. Rep. , 68 : 273 – 295 .
  • Rodkina , A. and Schurz , H. 2005 . Almost sure asymptotic stability of drift-implicit θ-methods for bilinear ordinary stochastic differential equations in ℝ1 . J. Comput. Appl. Math. , 180 : 13 – 31 . (doi:10.1016/j.cam.2004.09.060)
  • Shiryayev , A. N. 1996 . “ Probability ” . Berlin : Springer .
  • Wang , W. Q. and Chen , Y. P. 2011 . Mean-square stability of semi-implicit Euler method for nonlinear neutral stochastic delay differential equations . Appl. Numer. Math. , 61 : 696 – 701 . (doi:10.1016/j.apnum.2011.01.003)
  • Wu , F. , Mao , X. and Szpruch , L. 2010 . Almost sure exponential stability of numerical solutions for stochastic delay differential equations . Numer. Math. , 115 : 681 – 697 . (doi:10.1007/s00211-010-0294-7)
  • Z. Yu, Almost surely asymptotic stability of exact and numerical solutions for neutral stochastic pantograph equations, Abst. Appl. Anal. 2011 (2011), article id 143079, 14 p., doi:10.1155/2011/143079.
  • Z. Yu and M. Liu, Almost surely asymptotic stability of numerical solutions for neutral stochastic delay differential equations, Discrete Dyn. Nat. Soc. 2011 (2011), article id 217672, 11 p., doi:10.1155/2011/217672.

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