Weak Poincar´e Inequalities for Convergence Rate of Degenerate Diffusion Processes ∗

For a contraction C 0 -semigroup on a separable Hilbert space, the decay rate is es-timated by using the weak Poincar´e inequalities for the symmetric and anti-symmetric part of the generator. As applications, non-exponential convergence rate is character-ized for a class of degenerate diffusion processes, so that the study of hypocoercivity is extended. Concrete examples are presented.

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