The density evolution of McKean–Vlasov stochastic differential equations in the presence of an absorbing boundary is analysed where the solution to such equations corresponds to the dynamics of partially killed large populations. By using a fixed point theorem, we show that the density evolution is characterized as the solution of an integro-differential Fokker–Planck equation with Cauchy–Dirichlet data. This problem arises naturally within mean field game theory.

中文翻译：

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被杀死的麦基文-弗拉索夫过程的密度演化

分析了存在吸收边界的McKean-Vlasov随机微分方程的密度演化，其中该方程的解对应于部分被杀死的大种群的动力学。通过使用不动点定理，我们证明了密度演化的特征是具有Cauchy-Dirichlet数据的积分微分Fokker-Planck方程的解。在平均场博弈论中自然会出现这个问题。