Guangjie Li1, Qigui Yang2
|  J.F. Chassagneux, A. Jacquier and I. Mihaylov, An explicit Euler scheme with strong rate of convergence for financial SDEs with non-Lipschitz coefficients, SIAM J. Financial Math., 7(2016), 993-1021.
 X. Dai and A. Xiao, Numerical solutions of nonautonomous stochastic delay differential equations by discontinuous galerkin methods, J. Comput. Math., 37(2019), 421-438.
 D.J. Higham, X. Mao and C. Yuan, Almost sure and moment exponential stability in the numerical simulation of stochastic differential equations, SIAM J. Numer. Anal., 45(2007), 592-609.
 C. Huang, Mean square stability and dissipativity of two classes of theta methods for systems of stochastic delay differential equations, J. Comput. Appl. Math., 259(2014), 77-86.
 X. Mao, Almost sure exponential stability in the numerical simulation of stochastic differential equations, SIAM J. Numer. Anal., 53(2015), 370-389.
 Q. Yang and G. Li, Exponential stability of θ-method for stochastic differential equations in the G-framework, J. Comput. Appl. Math., 350(2019), 195-211.
 S. Gan, H. Schurz and H. Zhang, Mean square convergence of stochastic θ-methods for nonlinear neutral stochastic differential delay equations, Int. J. Numer. Anal. Model, 8(2011), 201-213.
 M. Milošević, Convergence and almost sure exponential stability of implicit numerical methods for a class of highly nonlinear neutral stochastic differential equations with constant delay, J. Comput. Appl. Math., 280(2015), 248-264.
 W. Wang and Y. Chen, Mean-square stability of semi-implicit Euler method for nonlinear neutral stochastic delay differential equations, Appl. Numer. Math., 61(2011), 696-701.
 H. Zhang and S. Gan, Mean square convergence of one-step methods for neutral stochastic differential delay equations, Appl. Math. Comput., 204(2008), 884-890.
 L. Liu and Q. Zhu, Mean square stability of two classes of theta method for neutral stochastic differential delay equations, J. Comput. Appl. Math., 305(2016), 55-67.
 X. Zong, F. Wu and C. Huang, Exponential mean square stability of the theta approximations for neutral stochastic differential delay equations, J. Comput. Appl. Math., 286(2015), 172-185.
 X. Mao and C. Yuan, Stochastic Differential Equations with Markovian Switching, London:Imperial College Press, 2006.
 B. Wang and Q. Zhu, Stability analysis of Markov switched stochastic differential equations with both stable and unstable subsystems, Systems Control Lett., 105(2017), 55-61.
 C. Yuan and X. Mao, Convergence of the Euler-Maruyama method for stochastic differential equations with Markovian switching, Math. Comput. Simulation, 64(2004), 223-235.
 Q. Zhu and Q. Zhang, P th moment exponential stabilization of hybrid stochastic differential equations by feedback controls based on discrete-timestate observations with a time delay, IET Control Theory Appl., 11(2017), 1992-2003.
 C. Huang, Exponential mean square stability of numerical methods for systems of stochastic differential equations, J. Comput. Appl. Math., 236(2012), 4016-4026.
 S. Rong, Theory of Stochastic Differential Equations with Jumps and Applications:Mathematical and Analytical Techniques with Applications to Engineering, Springer Science & Business Media, 2006.
 Y. Wei and Q. Yang, Dynamics of the stochastic low concentration trimolecular oscillatory chemical system with jumps, Nonlinear Sci. Numer. Simulat., 59(2018), 396-408.
 X. Zhang and K. Wang, Stochastic SEIR model with jumps, Appl. Math. Comput., 239(2014), 133-143.
 D. Liu, G. Yang and W. Zhang, The stability of neutral stochastic delay differential equations with Poisson jumps by fixed points, J. Comput. Appl. Math., 235(2011), 3115-3120.
 H. Mo, F. Deng and C. Zhang, Exponential stability of the split-step θ-method for neutral stochastic delay differential equations with jumps, Appl. Math. Comput., 315(2017), 85-95.
 H. Mo, X. Zhao and F. Deng, Exponential mean-square stability of the θ-method for neutral stochastic delay differential equations with jumps, Internat. J. Systems Sci., 48(2017), 462-470.
 M. Palanisamy and R. Chinnathambi, Approximate controllability of second-order neutral stochastic differential equations with infinite delay and Poisson jumps, J. Syst. Sci. Complex, 28(2015), 1033-1048.
 D. Applebaum, Lévy Processes and Stochastic Calculus, 2nd edn. Cambridge university press, 2009.
 D. Applebaum and M. Siakalli, Asymptotic stability of stochastic differential equations driven by Lévy noise, J. Appl. Probab., 46(2009), 1116-1129.
 X. Mao, Y. Shen and A. Gray, Almost sure exponential stability of backward Euler-Maruyama discretizations for hybrid stochastic differential equations, J. Comput. Appl. Math., 235(2011), 1213-1226.
 X. Mao, Stochastic Differential Equations and Application, Horwood Publication:Chichester, 1997.
|||Haiyan Yuan, Jihong Shen, Cheng Song. MEAN SQUARE STABILITY AND DISSIPATIVITY OF SPLITSTEP THETA METHOD FOR NONLINEAR NEUTRAL STOCHASTIC DELAY DIFFERENTIAL EQUATIONS WITH POISSON JUMPS [J]. Journal of Computational Mathematics, 2017, 35(6): 766-779.|