Monte Carlo Integration Using Elliptic Curves

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 Feynman-Kac formulas.

Keywords

Pseudorandom vectors / Elliptic curves / Finite fields / Monte Carlo integration / Feynman-Kac formulas

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