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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 128625, 8 pages
Numerical Analysis for Stochastic Partial Differential Delay Equations with Jumps
1Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
2College of Science, Huazhong Agriculture University, Wuhan 430074, China
3College of Mathematics and Statistics, South-Central University for Nationalities, Wuhan 430074, China
Received 3 January 2013; Accepted 21 March 2013
Academic Editor: Xuerong Mao
Copyright © 2013 Yan Li and Junhao Hu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- G. Da Prato and J. Zabczyk, Stochastic Equations in Infinite Dimensions, vol. 44 of Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, UK, 1992.
- K. Liu, Stability of Infinite Dimensional Stochastic Differential Equations with Applications, Chapman & Hall/CRC, Boca Raton, Fla, USA, 2004.
- Q. Luo, F. Deng, J. Bao, B. Zhao, and Y. Fu, “Stabilization of stochastic Hopfield neural network with distributed parameters,” Science in China F, vol. 47, no. 6, pp. 752–762, 2004.
- Q. Luo, F. Deng, X. Mao, J. Bao, and Y. Zhang, “Theory and application of stability for stochastic reaction diffusion systems,” Science in China F, vol. 51, no. 2, pp. 158–170, 2008.
- X. Mao, Stochastic Differential Equations and Applications, Horwood Publishing, Chichester, UK, 2007.
- Y. Shen and J. Wang, “An improved algebraic criterion for global exponential stability of recurrent neural networks with time-varying delays,” IEEE Transactions on Neural Networks, vol. 19, no. 3, pp. 528–531, 2008.
- Y. Shen and J. Wang, “Almost sure exponential stability of recurrent neural networks with markovian switching,” IEEE Transactions on Neural Networks, vol. 20, no. 5, pp. 840–855, 2009.
- I. Gyöngy and N. Krylov, “Accelerated finite difference schemes for linear stochastic partial differential equations in the whole space,” SIAM Journal on Mathematical Analysis, vol. 42, no. 5, pp. 2275–2296, 2010.
- A. Jentzen, P. E. Kloeden, and G. Winkel, “Efficient simulation of nonlinear parabolic SPDEs with additive noise,” The Annals of Applied Probability, vol. 21, no. 3, pp. 908–950, 2011.
- P. E. Kloeden, G. J. Lord, A. Neuenkirch, and T. Shardlow, “The exponential integrator scheme for stochastic partial differential equations: pathwise error bounds,” Journal of Computational and Applied Mathematics, vol. 235, no. 5, pp. 1245–1260, 2011.
- J. Bao, A. Truman, and C. Yuan, “Stability in distribution of mild solutions to stochastic partial differential delay equations with jumps,” Proceedings of The Royal Society of London A, vol. 465, no. 2107, pp. 2111–2134, 2009.
- B. Boufoussi and S. Hajji, “Successive approximation of neutral functional stochastic differential equations with jumps,” Statistics and Probability Letters, vol. 80, no. 5-6, pp. 324–332, 2010.
- E. Hausenblas, “Finite element approximation of stochastic partial differential equations driven by Poisson random measures of jump type,” SIAM Journal on Numerical Analysis, vol. 46, no. 1, pp. 437–471, 2007/08.
- S. Peszat and J. Zabczyk, Stochastic Partial Differential Equations with Lévy Noise: An Evolution Equation Approach, vol. 113 of Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, UK, 2007.
- M. Röckner and T. Zhang, “Stochastic evolution equations of jump type: existence, uniqueness and large deviation principles,” Potential Analysis, vol. 26, no. 3, pp. 255–279, 2007.
- J. Bao, B. Böttcher, X. Mao, and C. Yuan, “Convergence rate of numerical solutions to SFDEs with jumps,” Journal of Computational and Applied Mathematics, vol. 236, no. 2, pp. 119–131, 2011.
- N. Jacob, Y. Wang, and C. Yuan, “Numerical solutions of stochastic differential delay equations with jumps,” Stochastic Analysis and Applications, vol. 27, no. 4, pp. 825–853, 2009.
- A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, vol. 44 of Applied Mathematical Sciences, Springer, New York, NY, USA, 1983.