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

Deuschel, Jean-Dominique; Mazza, Christian

Ann. Appl. Probab. 4, No. 4, 1012-1056 (1994).

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.

Reviewer: D.Lepingle (Orléans)

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

Keywords:

Dirichlet forms; geometric bounds; Metropolis; nonsymmetric Markov chains; spectral gap; ultrametricity