Mode-Weighted Transport Certificates for State-Dependent Reflected Switching Diffusions
This work develops a computable transport-based condition to prove that state-dependent switching diffusions can be contractive in distribution, even if individual modes are expansive. It introduces a mode-weighted cost function that controls both continuous spatial moments and discrete mode mismatch probabilities. The result provides an explicit rate for global exponential contraction on $\mathbb{R}^n$ and compact convex domains with normal reflection.