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Title: Numerical schemes for effective calibration of elliptic and hypo-elliptic diffusions Authors:  Yuga Iguchi - University College London (United Kingdom) [presenting]
Alexandros Beskos - University College London (United Kingdom)
Matthew Graham - University College London (United Kingdom)
Abstract: Parametric inference for multi-variate diffusion processes requires using a numerical discretisation scheme as a proxy for the underlying intractable model. The choice of numerical schemes is critical in both likelihood-based inference and computational MCMC methods. Two weak second-order schemes are proposed as effective sampling tools for elliptic and hypo-elliptic diffusions in conjunction with a new closed-form approximation formula for the transition density of the underlying model. Due to consideration of higher-order weak approximation, the proposed schemes are, in general, conditionally non-Gaussian, as opposed to classical Gaussian-type schemes such as the Euler-Maruyama scheme that achieves a weak first-order convergence. The closed-form density approximation is derived by making use of Malliavin calculus in elliptic and hypo-elliptic settings and enables us to construct a (log) likelihood linked to the proposed schemes. Under both the high and low-frequency observations regime, analytical results associated with the weak second-order schemes showcase the effectiveness of the use of proposed schemes in the statistical calibration of diffusion processes compared to earlier works based upon Gaussian-type discretisation schemes.