Fractional boundary value problems lead to sticky diffusions with infinite mean time spent on the boundary.
D’Ovidio Fractional Boundary Value Problems and Elastic Sticky Brownian Motions, I: The half line
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Fractional Boundary Value Problems and elastic sticky Brownian motions, II: Non-local dynamic boundary conditions on smooth domains
Fractional boundary value problems lead to sticky diffusions with infinite mean time spent on the boundary.