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Going from a scaling approach for birth/death processes, we investigate thescaling limit of solutions to non-Markovian stochastic control problems bystudying the convergence of solutions to BSDEs driven a sequence of convergingmartingales. In particular we manage to describe how the values and optimalcontrols of control problems converge when the models converge towards acontinuous population model.

Scaling limit for stochastic control problems in population dynamics