A-m.s.-stable numerical methods for solving stochastic differential equations in the Ito-sense

In this paper we investigate the asymptotic mean-square stability (m.s.-stability) of the family of numerical methods for solving SDE's in the Ito-sense generalizing Rosenbrock's type methods. The connection between the asymptotic m.s.-stability of the numerical method for solving SDE and the absolute stability of the corresponding Rosenbrock's type method are...

artemev.pdf1.8 MB

Convergence of variational splines I

Strong convergence of interpolating splines on the imbedded meshes is established without the assumption that the system of operators corresponding to the added interpolation conditions is correct. It is also shown that correctness of the system of operators is equivalent to the zero intersection of their kernels.

The necessary...

rozhenko.pdf3.69 MB