arXiv:2008.08219 Abstract | arXiv Analytics

arXiv:2008.08219 [math.PR]Abstract References Reviews Resources

Monte Carlo construction of cubature on Wiener space

Published 2020-08-19Version 1

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 main result.

Comments: 21 pages

Categories: math.PR, cs.NA, math.NA

Keywords: wiener space, monte carlo construction, cubature formula, stochastic tchakaloffs theorem, stochastic differential equations

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