×

Convergence of numerical solutions to neutral stochastic delay differential equations with Markovian switching. (English) Zbl 1168.65007

The Euler-Maruyama method for neutral stochastic delay differential equation with Markovian switching is considered.

MSC:

65C30 Numerical solutions to stochastic differential and integral equations
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60H35 Computational methods for stochastic equations (aspects of stochastic analysis)
34K50 Stochastic functional-differential equations
34K28 Numerical approximation of solutions of functional-differential equations (MSC2010)
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Mao, Xue rong; Sabanis, Sotirios, Numerical solutions of SDDEs under local Lipschitz condition, Journal of computational and applied mathematics, 151, 215-227, (2003) · Zbl 1015.65002
[2] Mao, Xue rong, Numerical solutions of SFDEs under local Lipschitz condition, LMS journal computational mathematics, 6, 141-161, (2003)
[3] Yuan, Chenggui; Mao, Xuerong, Convergence of the euler – maruyama method for stochastic differential equation with Markovian switching, Mathematics and computer in simulation, 64, 223-235, (2004) · Zbl 1044.65007
[4] Li, Ronghua; Hou, Yingmin, Convergence and stability of numerical solutions to SDDEs with Markovian switching, Applied mathematics and computation, 175, 1080-1091, (2006) · Zbl 1095.65005
[5] Mao, Xue rong; Yuan, Chenggui, Approximations of the euler – maruyama type for sdewmss under non-Lipschitz condition, Journal of computational and applied mathematics, 151, 215-227, (2003)
[6] Ronghua, Li; Hongbing, Meng; Yonghong, Dai, Convergence of numerical solutions to SDDEs with jumps, Journal of computational and applied mathematics, 172, 584-602, (2003) · Zbl 1095.65006
[7] Li, Ronghua; Chang, Zhaoguang, Convergence of numerical solutions to SDDEs with Poisson jumps and Markovian switching, Journal of computational and applied mathematics, 184, 451-463, (2007) · Zbl 1120.65003
[8] Buchwar, Evelyn, Introduction of the numerical analysis of SDDE, Journal of computational and applied mathematics, 125, 297-307, (2000)
[9] Lamba, H.; Seaman, T., Mean-square stability properties of an adaptive time-stepping SDE solver, Journal of computational and applied mathematics, 194, 245-254, (2006) · Zbl 1098.65004
[10] Carletti, M., Numerical of stochastic differential problems in the biosciences, Journal of computational and applied mathematics, 185, 422-440, (2000) · Zbl 1077.65007
[11] Kolmanovskii, V.; Koroleva, N.; Maizenberg, T.; Mao, X.; Matasov, A., Neutral stochastic differential delay equation with Markovian switching, Stochastic analysis and application, 21, 4, 839-867, (2003) · Zbl 1025.60028
[12] Skorohod, A.V., Asymptotic methods in the theory of stochastic differential equations, (1989), American Mathematical Society Providence
[13] Wang, La-sheng; Xue, Hong, Convergence of numerical solutions to stochastic differential delay equations with Poisson jump and Markovian switching, Applied mathematics and computation, (2006) · Zbl 1128.65010
[14] Hu, Shigeng; Huang, Chengming, Stochastic differential equations, (2008), Science Publishing Beijing
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.