Explicit Milstein Schemes with Truncation for Nonlinear Stochastic Differential Equations


主讲人:李晓月 东北师范大学教授


地点:腾讯会议 539 449 081


主讲人介绍:李晓月,东北师范大学数学与统计学院教授,博士生导师,美国数学会评论员。长期从事随机微分方程稳定性理论、应用及数值逼近的研究, 在《SIAM J. Numer. Anal.》、 《SIAM J. Appl. Math.》、 《J. Differential Equations》、 《SIAM J. Control Optim.》、 《Math. Comp.》等国际高水平期刊上发表SCI论文30余篇。主持国家自然科学基金面上项目以及省部级项目多项。

内容介绍:Although some implicit numerical procedures have been developed to treat high nonlinearity, the question whether one can use explicit schemes to achieve convergence rate similar to that of Milstein's procedure remained open. This brings us to the current work that focuses on numerical solutions of stochastic differential equations using explicit schemes. Our main goals are to obtain order one convergence in the second moment in a finite-time interval. In contrast to the implicit schemes, explicit schemes are advantageous, easily implementable, and computationally less intensive. To overcome the difficulties due to super-linear growth of the coefficients, a truncation device is used in our algorithm. In addition to reaching aforementioned goals in the analysis part, numerical examples are provided to demonstrate our results.