Abstract
For a multi-dimensional diffusion process, an important problem is whether the associated basic adjoint relationship (BAR) uniquely characterizes the stationary distribution of the diffusion process. A key step in this characterization is an open problem that any solution to BAR does not change sign. This note describes the open problem precisely in the context of two classes of diffusion processes. They are semimartingale reflecting Brownian motions and piecewise Ornstein–Uhlenbeck processes.
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Dai, J.G., Dieker, A.B. Nonnegativity of solutions to the basic adjoint relationship for some diffusion processes. Queueing Syst 68, 295–303 (2011). https://doi.org/10.1007/s11134-011-9236-z
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DOI: https://doi.org/10.1007/s11134-011-9236-z
Keywords
- Diffusion approximations
- Heavy traffic limits
- Generalized Jackson networks
- Multiclass queueing networks
- Many-server queues
- Halfin–Whitt regime