  For numerical approximations to stochastic differential equations using the
Euler-Maruyama scheme, we propose incorporating approximate random variables
computed using low precisions, such as single and half precision. We propose
and justify a model for the rounding error incurred, and produce an average
case error bound for two and four way differences, appropriate for regular and
nested multilevel Monte Carlo estimations. By considering the variance
structure of multilevel Monte Carlo correction terms in various precisions with
and without a Kahan compensated summation, we compute the potential speed ups
offered from the various precisions. We find single precision offers the
potential for approximate speed improvements by a factor of 7 across a wide
span of discretisation levels. Half precision offers comparable improvements
for several levels of coarse simulations, and even offers improvements by a
factor of 10-12 for the very coarsest few levels.
