The pathwise convergence of approximation schemes for stochastic differential equations
P. E. Kloeden and A. Neuenkirch
Abstract: The authors of this paper study approximation methods for
stochastic differential equations, and point out a simple relation
between the order of convergence in the pth mean and
the order of convergence in the pathwise sense: Convergence in
the pth mean of order α for all p ≥ 1
implies pathwise convergence of order α − ε
for arbitrary ε > 0. The authors then apply this result to several
one-step and multi-step approximation schemes for stochastic
differential equations and stochastic delay differential
equations. In addition, they give some numerical examples.
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