We give a “direct” coupling proof of strict monotonicity of the speed for 1-dimensional multi-excited random walks with positive speed. This reproves (and extends) a recent result of Peterson without using branching processes.
"On strict monotonicity of the speed for excited random walks in one dimension." Electron. Commun. Probab. 20 1 - 7, 2015. https://doi.org/10.1214/ECP.v20-4212