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We propose a reformulation of the convergence theorem of monotone numericalschemes introduced by Zhang and Zhuo for viscosity solutions of path-dependentPDEs, which extends the seminal work of Barles and Souganidis on the viscositysolution of PDE. We prove the convergence theorem under conditions similar tothose of the classical theorem in the work of Barles and Souganidis. Theseconditions are satisfied, to the best of our knowledge, by all classicalmonotone numerical schemes in the context of stochastic control theory. Inparticular, the paper provides a unified approach to prove the convergence ofnumerical schemes for non-Markovian stochastic control problems, second orderBSDEs, stochastic differential games etc.

On the convergence of monotone schemes for path-dependent PDE