All Adapted Topologies are Equal

Understand

A number of researchers have introduced topological structures on the set of laws of stochastic processes.

• A unifying goal of these authors is to strengthen the usual weak topology in order to adequately capture the temporal structure of stochastic processes.
• Aldous defines an extended weak topology based on the weak convergence of prediction processes.
• In the economic literature, Hellwig introduced the information topology to study the stability of equilibrium problems.