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Stability of partially implicit Langevin schemes and their MCMC variants. (English) Zbl 1248.60080

Ergodicity properties of implicit and partially implicit discretization schemes for Langevin equations corresponding to a class of desired stationary distributions are established. It is shown that when used as a proposal for a Metropolis-Hastings scheme, the ergodicity properties are retained. A partially implicit scheme based on local linearization is also analyzed. Examples are provided. For ease of exposition, only the scalar case is considered.

MSC:

60H35 Computational methods for stochastic equations (aspects of stochastic analysis)
65C30 Numerical solutions to stochastic differential and integral equations
60J22 Computational methods in Markov chains
65C05 Monte Carlo methods
93E25 Computational methods in stochastic control (MSC2010)
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References:

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