In this paper we discuss two-stage Miistein methods for solving Ito stochastic differential equations （SDEs）. Six fully explicit methods （TSM 1 -- TSM 6） are given in this paper. Their order of strong convergence ...In this paper we discuss two-stage Miistein methods for solving Ito stochastic differential equations （SDEs）. Six fully explicit methods （TSM 1 -- TSM 6） are given in this paper. Their order of strong convergence is proved. The stability properties and numerical results show the effectiveness of these methods in the pathwise approximation of Ito SDEs.展开更多
In this paper, we construct a composite Milstein method for nonlinear stochastic differential delay equations. Then we analyze the mean square stability for this method and obtain the step size condition under which t...In this paper, we construct a composite Milstein method for nonlinear stochastic differential delay equations. Then we analyze the mean square stability for this method and obtain the step size condition under which the composite Milstein method is mean square stable. Moreover, we get the step size condition under which the composite Milstein method is global mean square stable. A nonlinear test stochastic differential delay equation is given for numerical tests. The results of numerical tests verify the theoretical results proposed.展开更多
基金the National Natural Science Foundation of China(11961029,11701237)the National Social Science Foundation of China(21CTJ018)+1 种基金the Scientific Research Project of Education Department of Hubei Province(D20212202)the Natural Science Foundation of Jiangxi Province(20202BABL201007)。
基金supported by the National Natural Science Foundation of China(10901106)the Natural Science Foundation of Shanghai Municipality,China(09ZR1423200)+2 种基金the Innovation Program of Shanghai Municipal Education Commission(09YZ150)the E-Institutes of Shanghai Municipal Education Commission(E03004)the Shanghai Leading Academic Discipline Project(S30405)
文摘In this paper we discuss two-stage Miistein methods for solving Ito stochastic differential equations （SDEs）. Six fully explicit methods （TSM 1 -- TSM 6） are given in this paper. Their order of strong convergence is proved. The stability properties and numerical results show the effectiveness of these methods in the pathwise approximation of Ito SDEs.
基金Supported by National Natural Science Foundation of China(No.61272024)Anhui Provincial Natural Science Foundation(No.11040606M06)
文摘In this paper, we construct a composite Milstein method for nonlinear stochastic differential delay equations. Then we analyze the mean square stability for this method and obtain the step size condition under which the composite Milstein method is mean square stable. Moreover, we get the step size condition under which the composite Milstein method is global mean square stable. A nonlinear test stochastic differential delay equation is given for numerical tests. The results of numerical tests verify the theoretical results proposed.
