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arXiv · 2008.08219

Monte Carlo construction of cubature on Wiener space

Satoshi Hayakawa·Ken'ichiro Tanaka
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Abstract

In this paper, we investigate application of mathematical optimization to construction of a cubature formula on Wiener space, which is a weak approximation method of stochastic differential equations introduced by Lyons and Victoir (Cubature on Wiener Space, Proc. R. Soc. Lond. A 460, 169--198). After giving a brief review of the cubature theory on Wiener space, we show that a cubature formula of general dimension and degree can be obtained through a Monte Carlo sampling and linear programming. This paper also includes an extension of stochastic Tchakaloff's theorem, which technically yields the proof of our primary result.

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Satoshi Hayakawa, Ken'ichiro Tanaka. 2020-08-19. Monte Carlo construction of cubature on Wiener space. https://doi.org/10.1007/s13160-021-00496-6

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