probability-statistics / Stochastic networks

Signed BAR Conjecture for Reflected Brownian Motion

Does the finite signed basic adjoint relation determine the invariant signed measure uniquely, and how far beyond the Harrison-Reiman class can uniqueness extend?

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probability-statisticsJul 3, 2026Significance 10/100Registry: unreviewed

Signed BAR Conjecture for Reflected Brownian Motion

Prior state unknownproved

uniqueness proved for stable Harrison-Reiman systems with a nonsingular M-matrix reflection; an infinite-dimensional obstruction is shown in the larger completely-S class

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Does the finite signed basic adjoint relation determine the invariant signed measure uniquely, and how far beyond the Harrison-Reiman class can uniqueness extend?

uniqueness proved for stable Harrison-Reiman systems with a nonsingular M-matrix reflection; an infinite-dimensional obstruction is shown in the larger completely-S class

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Signed BAR Conjecture for Reflected Brownian Motion — Mathematical Frontier Network