Guangjie Li^{1}, Qigui Yang^{2}
[1] J.F. Chassagneux, A. Jacquier and I. Mihaylov, An explicit Euler scheme with strong rate of convergence for financial SDEs with nonLipschitz coefficients, SIAM J. Financial Math., 7(2016), 9931021. [2] X. Dai and A. Xiao, Numerical solutions of nonautonomous stochastic delay differential equations by discontinuous galerkin methods, J. Comput. Math., 37(2019), 421438. [3] 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), 592609. [4] 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), 7786. [5] X. Mao, Almost sure exponential stability in the numerical simulation of stochastic differential equations, SIAM J. Numer. Anal., 53(2015), 370389. [6] Q. Yang and G. Li, Exponential stability of θmethod for stochastic differential equations in the Gframework, J. Comput. Appl. Math., 350(2019), 195211. [7] S. Gan, H. Schurz and H. Zhang, Mean square convergence of stochastic θmethods for nonlinear neutral stochastic differential delay equations, Int. J. Numer. Anal. Model, 8(2011), 201213. [8] 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), 248264. [9] W. Wang and Y. Chen, Meansquare stability of semiimplicit Euler method for nonlinear neutral stochastic delay differential equations, Appl. Numer. Math., 61(2011), 696701. [10] H. Zhang and S. Gan, Mean square convergence of onestep methods for neutral stochastic differential delay equations, Appl. Math. Comput., 204(2008), 884890. [11] 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), 5567. [12] 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), 172185. [13] X. Mao and C. Yuan, Stochastic Differential Equations with Markovian Switching, London:Imperial College Press, 2006. [14] B. Wang and Q. Zhu, Stability analysis of Markov switched stochastic differential equations with both stable and unstable subsystems, Systems Control Lett., 105(2017), 5561. [15] C. Yuan and X. Mao, Convergence of the EulerMaruyama method for stochastic differential equations with Markovian switching, Math. Comput. Simulation, 64(2004), 223235. [16] Q. Zhu and Q. Zhang, P th moment exponential stabilization of hybrid stochastic differential equations by feedback controls based on discretetimestate observations with a time delay, IET Control Theory Appl., 11(2017), 19922003. [17] C. Huang, Exponential mean square stability of numerical methods for systems of stochastic differential equations, J. Comput. Appl. Math., 236(2012), 40164026. [18] S. Rong, Theory of Stochastic Differential Equations with Jumps and Applications:Mathematical and Analytical Techniques with Applications to Engineering, Springer Science & Business Media, 2006. [19] Y. Wei and Q. Yang, Dynamics of the stochastic low concentration trimolecular oscillatory chemical system with jumps, Nonlinear Sci. Numer. Simulat., 59(2018), 396408. [20] X. Zhang and K. Wang, Stochastic SEIR model with jumps, Appl. Math. Comput., 239(2014), 133143. [21] 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), 31153120. [22] H. Mo, F. Deng and C. Zhang, Exponential stability of the splitstep θmethod for neutral stochastic delay differential equations with jumps, Appl. Math. Comput., 315(2017), 8595. [23] H. Mo, X. Zhao and F. Deng, Exponential meansquare stability of the θmethod for neutral stochastic delay differential equations with jumps, Internat. J. Systems Sci., 48(2017), 462470. [24] M. Palanisamy and R. Chinnathambi, Approximate controllability of secondorder neutral stochastic differential equations with infinite delay and Poisson jumps, J. Syst. Sci. Complex, 28(2015), 10331048. [25] D. Applebaum, Lévy Processes and Stochastic Calculus, 2nd edn. Cambridge university press, 2009. [26] D. Applebaum and M. Siakalli, Asymptotic stability of stochastic differential equations driven by Lévy noise, J. Appl. Probab., 46(2009), 11161129. [27] X. Mao, Y. Shen and A. Gray, Almost sure exponential stability of backward EulerMaruyama discretizations for hybrid stochastic differential equations, J. Comput. Appl. Math., 235(2011), 12131226. [28] X. Mao, Stochastic Differential Equations and Application, Horwood Publication:Chichester, 1997. 
[1]  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): 766779. 
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