Convergence of Numerical Solutions to Stochastic Delay Neural Networks with Poisson Jump and Markovian Switching

Hong Ge Yue; Qi Min Zhang

doi:10.4028/www.scientific.net/AMR.219-220.1153

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HomeAdvanced Materials ResearchAdvanced Materials Research Vols. 219-220Convergence of Numerical Solutions to Stochastic...

Convergence of Numerical Solutions to Stochastic Delay Neural Networks with Poisson Jump and Markovian Switching

Abstract:

In general stochastic delay neural networks with Poisson jump and Markovian switching do not have explicit solutions. Appropriate numerical approximations, such as the Euler scheme, are therefore a vital tool in exploring their properties. Unfortunately, the numerical methods for stochastic delay neural networks with Poisson jump and Markovian switching (SDNNwPJMSs) have never been studied. In this paper we proved that the Euler approximate solutions will converge to the exact solutions for SDNNwPJMSs under local Lipschitz condition. This result is more general than what they deal with the Markovian switching term or the jump term.

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Advanced Materials Research (Volumes 219-220)

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1153-1157

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https://doi.org/10.4028/www.scientific.net/AMR.219-220.1153

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March 2011

Authors:

Hong Ge Yue, Qi Min Zhang

Keywords:

Euler Scheme, Local Lipschitz Condition, Markovian Switching, Poisson Jump

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References

[1] X. Mao, Stability of stochastic differential equations with Markovian switching, Stochast. Process. Appl.79(1999)45-67.

Google Scholar

[2] X.Mao, A.Matasov, A.B. Piunovskiy, Stochastic differential delay equations with Markovian switching, Bernoulli 6(1)(2000)73-90.

DOI: 10.2307/3318634

Google Scholar

[3] G. Marion, X. Mao, E. Renshaw, Convergence of the Euler scheme for a class of stochastic differential, Int.Math. J.1 (1)(2002)9-22.

Google Scholar

[4] D.J. Higham, P.E. Kloeden, Numerical methods for nonlinear stochastic differential equations with Jumps, University of Strathclyde Mathematics Research Report, vol.13,(2004).

Google Scholar

[5] D.J. Higham, P.E. Kloeden, Convergence and stability of implicit methods for jump-diffusion systems, University of Strathclyde Mathematics Research Report, vol. 9, (2004).

Google Scholar

[6] Xuerong Mao, Sotirios Sabanis, Numerical solutions of stochastic differential delay equations under local Lipschitz condition,J. Comput. Appl. Math. 151 (2003) 215-227.

DOI: 10.1016/s0377-0427(02)00750-1

Google Scholar

[7] Li Ronghua,Meng Hongbing, Dai Yonghong, Convergence of numerical solutions to stochastic delay differential equations with jumps, J. Comput. Appl.Math. 172 (2006) 584-602.

DOI: 10.1016/j.amc.2005.02.017

Google Scholar

[8] Li Ronghua, Hou Yingmin,Convergence and stability of numerical solutions to SDDEs with Markovian switching, J. Appl. Math. Comput. 175 (2006) 1080-1091.

DOI: 10.1016/j.amc.2005.08.026

Google Scholar

[9] A.V. Svishchuk, Yu.I. Kazmerchuk, Stability of stochastic delay equations of It form with jumps and Markovian switchings, and their applications in finance, Theor.Probab. Math. Stat. 64 (2002) 167-178.

Google Scholar

[10] La-sheng Wang, Hong Xue, Convergence of numerical solutions to stochastic differential delay equations with Poisson jump and Markovian switching, Applied Mathematics and Computation, 188(2007)1161-1172.

DOI: 10.1016/j.amc.2006.10.058

Google Scholar