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| Monte Carlo Integration Using Elliptic Curves |
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Citation： |
Chung Pang MOK,Huimin ZHENG.Monte Carlo Integration Using Elliptic Curves[J].Chinese Annals of Mathematics B,2025,46(2):241~260 |
| Page view： 462
Net amount： 170 |
Authors： |
Chung Pang MOK; Huimin ZHENG |
Foundation： |
the National Natural Science Foundation of China (Nos. 11571163,
12231009), the Key Special Project on Key Scientific Issues of Transformational Technology (No.
SQ2020YFA070208) and the Ministry of Science and Technology of Suzhou (No. ZXL2021458). |
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| Abstract： |
The authors carry out numerical experiments with regard to the Monte Carlo
integration method, using as input the pseudorandom vectors that are generated by the
algorithm proposed in [Mok, C. P., Pseudorandom Vector Generation Using Elliptic Curves
and Applications to Wiener Processes, Finite Fields and Their Applications, 85, 2023,
102129], which is based on the arithmetic theory of elliptic curves over finite fields. They
consider integration in the following two cases: The case of Lebesgue measure on the
unit hypercube [0, 1]d, and as well as the case of Wiener measure. In the case of Wiener
measure, the construction gives discrete time simulation of an independent sequence of
standard Wiener processes, which is then used for the numerical evaluation of FeynmanKac formulas. |
Keywords： |
Pseudorandom vectors Elliptic curves Finite fields Monte Carlo
integration Feynman-Kac formulas |
Classification： |
11K45, 65C10, 65C05, 65M75 |
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