Particle-based likelihood inference in partially observed diffusion processes using generalised Poisson estimators. (English) Zbl 1274.62564

Summary: This paper concerns the use of the expectation-maximisation (EM) algorithm for inference in partially observed diffusion processes. In this context, a well known problem is that all except a few diffusion processes lack closed-form expressions of the transition densities. Thus, in order to estimate efficiently the EM intermediate quantity we construct, using novel techniques for unbiased estimation of diffusion transition densities, a random weight fixed-lag auxiliary particle smoother, which avoids the well known problem of particle trajectory degeneracy in the smoothing mode. The estimator is justified theoretically and demonstrated on a simulated example.


62M09 Non-Markovian processes: estimation
65C05 Monte Carlo methods
Full Text: DOI arXiv Euclid


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