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On McKean-Vlasov Branching Diffusion Processes
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We study a nonlinear branching diffusion process in the sense of McKean, i.e., where particles are subjected to a mean-field interaction. We consider first a strong formulation of the problem and we provide an existence and uniqueness result by using contraction arguments. Then we consider the notion of weak solution and its equivalent martingale problem formulation. In this setting, we provide a general weak existence result, as well as a propagation of chaos property, i.e., the McKean-Vlasov branching diffusion is the limit of a large population branching diffusion process with mean-field interaction.
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Optimal Control of McKean--Vlasov Branching Diffusion Processes
For closed-loop controlled McKean-Vlasov branching diffusions, the value function is characterized by an HJB master equation on finite measures, with an explicit linear-quadratic example.
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