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MCMC methods for diffusion bridges. (English) Zbl 1159.65007

This interesting work may be useful for the specialists in various subjects: Markov chain Monte Carlo (MCMC) methods; stochastic partial differential equations (SPDEs), and SDEs on Hilbert space; implicit schemes for SPDEs; and relevant numerical studies.
The authors present and study a Langevin MCMC approach for sampling nonlinear diffusion bridges. The proposed moves for the MCMC algorithm are determined by discretising the SPDEs. Of all innovations the part, which deals with implicit schemes for Langevin SPDEs, is the key one. The only one value of the scheme parameter is proved to be good, and the authors study this fact in detail, including the numerical examples.
Several adjoining themes are considered briefly, for example, a random-walk Metropolis and an independence sampler on the pathspace.

MSC:

65C30 Numerical solutions to stochastic differential and integral equations
65C05 Monte Carlo methods
60H35 Computational methods for stochastic equations (aspects of stochastic analysis)
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
35R60 PDEs with randomness, stochastic partial differential equations
65C40 Numerical analysis or methods applied to Markov chains
60G50 Sums of independent random variables; random walks
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References:

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