Recent results on multiplicative noise

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Abstract
Recent developments in the analysis of Langevin equations with multiplicative noise (MN) are reported. In particular, we (i) present numerical simulations in three dimensions showing that the MN equation exhibits, like the Kardar-Parisi-Zhang (KPZ) equation, both a weak coupling fixed point and a strong coupling phase, supporting the proposed relation between MN and KPZ; (ii) present a dimensional and mean-field analysis of the MN equation to compute critical exponents; (iii) show that the phenomenon of the noise-induced ordering transition associated with the MN equation appears only in the Stratonovich representation and not in the Ito one; and (iv) report the presence of a first-order-like phase transition at zero spatial coupling, supporting the fact that this is the minimum model for noise-induced ordering transitions.