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arXiv · 2210.13530

An efficient Monte Carlo scheme for Zakai equations

Christian Beck·Sebastian Becker·Patrick Cheridito·Arnulf Jentzen·Ariel Neufeld
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Abstract

In this paper we develop a numerical method for efficiently approximating solutions of certain Zakai equations in high dimensions. The key idea is to transform a given Zakai SPDE into a PDE with random coefficients. We show that under suitable regularity assumptions on the coefficients of the Zakai equation, the corresponding random PDE admits a solution random field which, for almost all realizations of the random coefficients, can be written as a classical solution of a linear parabolic PDE. This makes it possible to apply the Feynman--Kac formula to obtain an efficient Monte Carlo scheme for computing approximate solutions of Zakai equations. The approach achieves good results in up to 25 dimensions with fast run times.

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Christian Beck, Sebastian Becker, Patrick Cheridito, Arnulf Jentzen, Ariel Neufeld. 2022-10-24. An efficient Monte Carlo scheme for Zakai equations. https://doi.org/10.1016/j.cnsns.2023.107438

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