Two adapted stochastic processes can have similar laws but give different results in applications such as optimal stopping, queuing theory, or programming. The reason is that the topology of weak convergence does not account for growth information over time captured filtration an process. To address discontinuities, Aldous introduced extended topology, and subsequently, Hoover Keisler showed bo...

A number of researchers have independently introduced topologies on the set laws stochastic processes that extend usual weak topology. Depending respective scientific background this was motivated by applications and connections to various areas (e.g., Plug–Pichler—stochastic programming, Hellwig—game theory, Aldous—stability optimal stopping, Hoover–Keisler—model theory). Remarkably, all these...