Stochastically stable one-step approximations of solutions of stochastic ordinary differential equations
by
Roža Horvat Bokor

A series of numerical methods (schemes) for solving stochastic ordinary differential equations (SODEs) were developed. Under appropriate conditions the numerical solutions converge in mean square sense to the true solution. There is a general belief, supported by theorems for the Euler-Maruyama and Milstein methods that the above statement implies the stochastic stability i.e. the continuous dependence on initial values of the numerical solutions. In this talk this assertion is rigorously proved for methods widely used, but not investigated from this aspect.

Date received: March 18, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caex-38.