## $$L^ 2$$ convergence of time nonhomogeneous Markov processes. I: Spectral estimates.(English)Zbl 0819.60063

Methods based on Dirichlet forms and geometric techniques are used to estimate the rate of convergence in nonsymmetric annealing processes. One main result is that the true and symmetrized spectral gaps are logarithmically equivalent. Some robust estimates for the gap are also given, and the case of diffusions on a compact manfiold with small noise is investigated.

### MSC:

 60J27 Continuous-time Markov processes on discrete state spaces 60F10 Large deviations 93E25 Computational methods in stochastic control (MSC2010) 15A18 Eigenvalues, singular values, and eigenvectors 60J60 Diffusion processes
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