Mathematics Seminar 02/04/22

Abstract: We propose and study a numerical method for solving stochastic differential equations in which the drift coefficient satisfies some piece-wise regularity conditions and the diffusion coefficient is Lipschitz continuous and non-degenerate at the discontinuity points of the drift coefficient, if exist. In the case where the the drift coefficient is discontinuous, we construct an adaptive step function for the quasi - Milstein scheme. Our scheme is proved to have strong convergence of order 1 with respect to the average computational cost. We support our theoretical findings by computing and comparing the convergence rate for some numerical examples.

For more information, please contact  Dr. Vu Thai Luan: luan@math.msstate.edu ; (662)-325-7162.