论文标题
用于测量值人群动力学及其大型人口限制的广义梯度结构
Generalized gradient structures for measure-valued population dynamics and their large-population limit
论文作者
论文摘要
我们考虑到与人群动态中一类相互作用的粒子系统所源自的测量值的过程相对应的前向kolmogorov方程，包括bolker-pacala-dieckmann-law模型的变化。在详细平衡的假设下，我们提供了严格的广义梯度结构，并结合了颗粒的出生和死亡引起的通量。 此外，在较大的人口限制中，我们显示了向前的kolmogorov方程与liouville方程的融合，该方程是与基础过程的平均场限制相关的传输方程。此外，我们从能量散落原理的意义上显示了相应梯度结构的收敛性，从中我们为粒子系统建立了混乱结果的传播，并得出了平均场限制的广义梯度流式公式。
We consider the forward Kolmogorov equation corresponding to measure-valued processes stemming from a class of interacting particle systems in population dynamics, including variations of the Bolker-Pacala-Dieckmann-Law model. Under the assumption of detailed balance, we provide a rigorous generalized gradient structure, incorporating the fluxes arising from the birth and death of the particles. Moreover, in the large population limit, we show convergence of the forward Kolmogorov equation to a Liouville equation, which is a transport equation associated with the mean-field limit of the underlying process. In addition, we show convergence of the corresponding gradient structures in the sense of Energy-Dissipation Principles, from which we establish a propagation of chaos result for the particle system and derive a generalized gradient-flow formulation for the mean-field limit.
