Weak* Convergence and the Prohorov Metric in Inverse Problems

We turn next to discuss functional analysis concepts (in particular the concept of weak* convergence introduced in Section 4.2) that are integral to several types of inverse problems. These problems entail parameter estimation using output observations where the parameters to be estimated are probability distributions. Such problems can be readily found in certain areas of applications [BBi, BBH, BBKW, BBPP, BD, BDTR, GRD-FP, BDEHAD, GRD-FP2, BF, BFPZ, BG1, BG2, BGIT]. Here we consider two types of measure dependent problems: individual dynamics and aggregate dynamics.