A 'Dual'-Improved Shortcut To The Long Run

The author uses the theories of duality and optimal branchings to find a necessary and sufficient characterization of Stochastically Stable Limit Sets (SSLS) that helps improve the radius - modified coradius test of Ellison (2000). The improved shortcut the author offers may permit the identification of SSLS when Ellison's radius - modified coradius test fails to identify any, or may be able to pinpoint the true SSLS in cases where Ellison's test identifies only a superset. The author also demonstrates precisely why the radius - modified coradius test is not universally applicable and illuminates the connection between the modified coradius and the Lagrange multipliers of the optimal branching problem.