On the stability of the linear Skorohod problem in an orthant

Abstract.

Dupuis and Williams proved that a sufficient condition for the positive recurrence for a semimartingale reflecting Brownian motion in an orthant (SRBM) with data (θ, R, S, Δ), is that the corresponding Linear Skorohod Problem LSP (θ) is stable. In this paper we use the linear complementary problem to give necessary conditions, on θ∈ℝⁿ and matrix R, under which the linear Skorohod problem LSP (θ) is stable. In the three dimensional case we characterize the vectors θ∈ℝ³ such that the LSP (θ) is stable.