On Two-Step Methods for Stochastic

  Differential Equations

Rózsa Horváth Bokor 1 2

Abstract

 The paper introduces a new two-step method. Its order of strong convergence is proved. In the approximation of solutions of some stochastic differential equations, this multistep method converges faster in mean E |X-YN| than the One-step Milstein scheme with order 1.0 or Two-step Milstein scheme with order 1.0.

Footnotes:

  1 Department of Mathematics University of Zagreb, Bijemicka 30, 10000 Zagreb, Croatia, email: bokor@math.hr

  2 Work supported by the Central Research Found of the Hungarian Academy of Sciences (Grant No. T014548)