Unbiased estimation using a class of diffusion processes

Ruzayqat, Hamza; Beskos, Alexandros; Crisan, Dan; Jasra, Ajay; Kantas, Nikolas

doi:10.1016/j.jcp.2022.111643

Journal of Computational Physics

2023

DOI: 10.1016/j.jcp.2022.111643

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Unbiased estimation using a class of diffusion processes

Hamza Ruzayqat

Alexandros Beskos

Dan Crisan

et al.

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Cited by 3 publications

References 15 publications

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Antithetic multilevel particle filters

Jasra,

Maama,

Ombao

2024

Adv. Appl. Probab.

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In this paper we consider the filtering of partially observed multidimensional diffusion processes that are observed regularly at discrete times. This is a challenging problem which requires the use of advanced numerical schemes based upon time-discretization of the diffusion process and then the application of particle filters. Perhaps the state-of-the-art method for moderate-dimensional problems is the multilevel particle filter of Jasra et al. (SIAM J. Numer. Anal.55 (2017), 3068–3096). This is a method that combines multilevel Monte Carlo and particle filters. The approach in that article is based intrinsically upon an Euler discretization method. We develop a new particle filter based upon the antithetic truncated Milstein scheme of Giles and Szpruch (Ann. Appl. Prob.24 (2014), 1585–1620). We show empirically for a class of diffusion problems that, for $\epsilon>0$ given, the cost to produce a mean squared error (MSE) of $\mathcal{O}(\epsilon^2)$ in the estimation of the filter is $\mathcal{O}(\epsilon^{-2}\log(\epsilon)^2)$ . In the case of multidimensional diffusions with non-constant diffusion coefficient, the method of Jasra et al. (2017) requires a cost of $\mathcal{O}(\epsilon^{-2.5})$ to achieve the same MSE.

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Antithetic multilevel particle filters

Jasra,

Maama,

Ombao

2024

Adv. Appl. Probab.

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Global Optimization via Schrödinger–Föllmer Diffusion

Dai,

Jiao,

Kang

et al. 2023

SIAM J. Control Optim.

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Unbiased Estimation Using Underdamped Langevin Dynamics

Ruzayqat,

Chada,

Jasra

2023

SIAM J. Sci. Comput.

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Unbiased estimation using a class of diffusion processes

Cited by 3 publications

References 15 publications

Antithetic multilevel particle filters

Antithetic multilevel particle filters

Global Optimization via Schrödinger–Föllmer Diffusion

Unbiased Estimation Using Underdamped Langevin Dynamics

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