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Parameter inference for stochastic differential equations with density tracking by quadrature. (English) Zbl 1397.62077
Pilz, Jürgen (ed.) et al., Statistics and simulation. Contributions given at the 8th international workshop on simulation, IWS 8, Vienna, Austria, September 21–25, 2015. Cham: Springer (ISBN 978-3-319-76034-6/hbk; 978-3-319-76035-3/ebook). Springer Proceedings in Mathematics & Statistics 231, 99-113 (2018).
Summary: We derive and experimentally test an algorithm for maximum likelihood estimation of parameters in stochastic differential equations (SDEs). Our innovation is to efficiently compute the transition densities that form the log likelihood and its gradient, and to then couple these computations with quasi-Newton optimization methods to obtain maximum likelihood estimates. We compute transition densities by applying quadrature to the Chapman-Kolmogorov equation associated with a time discretization of the original SDE. To study the properties of our algorithm, we run a series of tests involving both linear and nonlinear SDE. We show that our algorithm is capable of accurate inference, and that its performance depends in a logical way on problem and algorithm parameters.
For the entire collection see [Zbl 1398.62008].

62F03 Parametric hypothesis testing
34F05 Ordinary differential equations and systems with randomness
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
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