Mean Square Convergence of the Numerical Solution of Random Differential Equations

Arciniega A.: Shooting methods for numerical solution of nonlinear stochastic boundary-value problems. Stoch. Anal. Appl. 25, 187–200 (2007)

Basu A., Ghosh M.K.: Stochastic differential games with multiple modes and applications to portfolio optimization. Stoch. Anal. Appl. 25, 845–867 (2007)

Brugnano L., Burrage K., Burrage P.M.: Adams-type methods for the numerical solution of stochastic ordinary differential equations. BIT 40, 451–470 (2000)

Brugnano L., Carreras G., Burrage K.: On the convergence of LMF-type methods for SODEs. Mediterr. J. Math. 1, 297–313 (2004)

Burden, R.L., Faires, J.D.: Numerical Analysis, 9th edn. Brooks-Cole, Cengage Learning (2010)

Burrage K., Burrage P.M.: Order conditions of stochastic Runge–Kutta methods by B-series. SIAM J. Numer. Anal. 38, 1626–1646 (2000)

Calbo G., Cortes J.C., Jodar L.: Mean square power series solution of random linear differential equations. Comput. Math. Appl. 59, 559–572 (2010)

Cortes J.C., Jodar L., Villafuerte L.: Mean square numerical solution of random differential equations: facts and possibilities. Comput. Math. Appl. 53, 1098–1106 (2007)

Cortes J.C., Jodar L., Villafuerte L.: Numerical solution of random differential equations: a mean square approach. Math. Comput. Model. 45, 757–765 (2007)

Guo C., O’Regan D., Deng F., Agarwal R.P.: Fixed points and exponential stability for a stochastic neutral cellular neural network. Appl. Math. Lett. 26, 849–853 (2013)

Khodabin M., Maleknejad K., Rostami M., Nouri M.: Numerical solution of stochastic differential equations by second order Runge–Kutta methods. Math. Comput. Model. 53, 1910–1920 (2011)

Kloeden, P.E., Platen, E.: Numerical Solution of Stochastic Differential Equations, 3rd edn. Springer, Berlin (1999)

Ladde G.S., Lakshmikantham V.: Random Differential Inequalities. Academic Press, New York (1980)

Mao X.: Stochastic Differential Equations and Their Applications. Horwood, New York (1997)

Maticiuc L., Rotenstein E.: Numerical schemes for multivalued backward stochastic differential systems. Cent. Eur. J. Math. 10, 693–702 (2012)

Oksendal, B.: Stochastic Differential Equations, an Introduction with Applications, 6th edn. Springer, Berlin (2003)

Soong T.T.: Random Differential Equations in Science and Engineering. Academic Press, New York (1973)

Stojanovic M.: Wave equation driven by fractional generalized stochastic processes. Mediterr. J. Math. 10, 1813–1831 (2013)

Wu F., Mao X., Kloeden P.E.: Almost sure and moment exponential stability of the Euler–Maruyama approximate solutions to stochastic functional differential equations. Discrete Conts. Dyn. Syst. Ser. A 33, 885–903 (2013)