Discoveries / probability-statistics

The Signed BAR Uniqueness Problem

For a multidimensional reflected diffusion, does the basic adjoint relationship uniquely characterize the stationary distribution? The question had stood unresolved for more than thirty-five years since the BAR approach was introduced. For stable Harrison-Reiman data with a nonsingular $M$-matrix reflection matrix, the finite-signed uniqueness problem is settled, via pathwise differentiability of the reflected process; the nonsigned version is also shown unique within the Harrison-Reiman class.