  Reaction-diffusion systems which include processes of the form A+A->A or
A+A->0 are characterised by the appearance of `imaginary' multiplicative noise
terms in an effective Langevin-type description. However, if `real' as well as
`imaginary' noise is present, then competition between the two could
potentially lead to novel behaviour. We thus investigate the asymptotic
properties of the following two `mixed noise' reaction-diffusion systems. The
first is a combination of the annihilation and scattering processes 2A->0,
2A->2B, 2B->2A, and 2B->0. We demonstrate (to all orders in perturbation
theory) that this system belongs to the same universality class as the single
species annihilation reaction 2A->0. Our second system consists of competing
annihilation and fission processes, 2A->0 and 2A->(n+2)A, a model which
exhibits a transition between active and absorbing phases. However, this
transition and the active phase are not accessible to perturbative methods, as
the field theory describing these reactions is shown to be non-renormalisable.
This corresponds to the fact that there is no stationary state in the active
phase, where the particle density diverges at finite times. We discuss the
implications of our analysis for a recent study of another active / absorbing
transition in a system with multiplicative noise.
