Year: 2026
Type: preprint
Abstract: We establish a local-minorization criterion for diffusions with countably many state-dependent switching regimes, even when every frozen transition law is singular. One regular controlled path yields a common absolutely continuous component for nearby initial states, with rate positivity required only at the switching locations. The proof controls a family of Brownian perturbations and its derivatives while retaining a path restriction for the switching likelihood. Controlled entrance and a joint Lyapunov inequality then give weighted exponential ergodicity. A concrete coefficient and rank criterion and degenerate network examples illustrate the result.
Source: arXiv (Cornell University)
Author: Cheng, Yuzhong
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223147285