References
- D.J. Higham and P.E. Kloeden, Strong convergence rates for backward Euler on a class of nonlinear jump-diffusion problems, J. Comput. Appl. Math. 205 (2007), pp. 949–956. doi: 10.1016/j.cam.2006.03.039
- D.J. Higham, X. Mao, and A.M. Stuart, Strong convergence of Euler-type methods for nonlinear stochastic differential equations, SIAM J. Numer. Anal. 40 (2003), pp. 1041–1063. doi: 10.1137/S0036142901389530
- Y. Hu, Semi-Implicit Euler–Maruyama Scheme for Stiff Stochastic Equations, Birkhäuser, Boston, 1996.
- V. Kolmanovskii and A. Myshkis, Applied Theory of Functional Differential Equations, Kluwer Academic Publishers, Dordrecht, 1992.
- G.S. Ladde and V. Lakshmikantham, Random Differential Inequalities, Academic Press, New York, 1980.
- Q. Luo, X. Mao, and Y. Shen, Generalised theory on asymptotic stability and boundedness of stochastic functional differential equations, Automatica. 47 (2011), pp. 2075–2081. doi: 10.1016/j.automatica.2011.06.014
- X. Mao, Exponential stability in mean square of neutral stochastic differential functional equations, Syst. Control Lett. 26 (1996), pp. 245–251. doi: 10.1016/0167-6911(95)00018-5
- X. Mao, Numerical solutions of stochastic functional differential equations, LMS J. Comput. Math. 6 (2003), pp. 1821–1841. doi: 10.1112/S1461157000000425
- X. Mao, Stochastic Differential Equations and Applications, 2nd ed., Horwood, Chichester, UK, 2007.
- X. Mao, Approximate solutions for a class of stochastic evolution equations with variable delays, Numer. Func. Anal. Opt. 12 (2007), pp. 525–533. doi: 10.1080/01630569108816448
- X. Mao, The truncated Euler–Maruyama method for stochastic differential equations, J. Comput. Appl. Math. 290 (2015), pp. 370–384. doi: 10.1016/j.cam.2015.06.002
- X. Mao, Convergence rates of the truncated Euler–Maruyama method for stochastic differential equations, J. Comput. Appl. Math. 296 (2016), pp. 362–375. doi: 10.1016/j.cam.2015.09.035
- X. Mao and C. Yuan, Stochastic Differential Equations with Markovian Switching, Imp. Coll. Press, London, 2006.
- X. Mao, C. Yuan, and J. Zou, Stochastic differential delay equations of population dynamics, J. Math. Anal. Appl. 304 (2005), pp. 296–320. doi: 10.1016/j.jmaa.2004.09.027
- M. Song, L. Hu, X. Mao, and L. Zhang, Khasminskii-type theorems for stochastic functional differential equations, Disc. Cont. Dyn. Syst. B 6 (2013), pp. 1697–1714. doi: 10.3934/dcdsb.2013.18.1697