Marianne Akian - Institut National de Recherche en Informatique et Automatique (INRIA) We consider Hamilton-Jacobi-Bellman equations associated to diffusion control problems involving a finite set-valued (or switching) control and possibly a continuum-valued control. We develop several lower complexity probabilistic numerical algorithms for such equations by combining max-plus and numerical probabilistic approaches. For deterministic optimal control problems, the max-plus approach is using the max-plus linearity of the Lax-Oleinik operator associated to the Hamilton-Jacobi equation. A stochastic max-plus approach has been introduced by Z. Qu (2013) for deterministic control problems. We shall compare it with the stochastic dual dynamic programming method which is used in the context of discrete time problems. For stochastic control problems, we can use a max-plus approach in the spirit of the one of McEneaney, Kaise and Han (2011), which is based on the distributivity of monotone operators with respect to suprema. We show how to combine it with a numerical probabilistic approach obtained by improving the one proposed by Fahim, Touzi and Warin (2011) in such a way that it satisfies a monotonicity property. This talk is based joint works with Jean-Philippe Chancelier, Benoît Tran and Eric Fodjo.