Numerical Analysis of equivariant evolution equations
09-034 Wolf-Jürgen Beyn, Raphael Kruse.
Two-Sided Error Estimates for the
Stochastic Theta Method
Two-sided error estimates are derived for the strong error of convergence
of the stochastic theta method. The main result is based on two
ingredients. The first one shows how the theory of convergence can be embedded
into standard concepts of consistency, stability and convergence by an
appropriate choice of norms and function spaces. The second one is a suitable
stochastic generalization of Spijker's norm (1968) that is known to lead to
two-sided error estimates for deterministic one-step methods. We show that
the stochastic theta method is bistable with respect to this norm and that
well-known results on the optimal O(√h) order of convergence follow from
this property in a natural way.
