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Aim of this paper is to extend the continuous dependence estimates proved in\cite{JK1} to quasi-monotone systems of fully nonlinear second-order parabolicequations. As by-product of these estimates, we get an H\"older estimate forbounded solutions of systems and a rate of convergence estimate for thevanishing viscosity approximation. In the second part of the paper we employsimilar techniques to study the periodic homogenization of quasi-monotonesystems of fully nonlinear second-order uniformly parabolic equations. Finally,some examples are discussed.

Continuous dependence estimates and homogenization of quasi-monotone systems of fully nonlinear second order parabolic equations