Infinite-Dimensional Monte Carlo Integration
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چکیده
In mathematics, Monte Carlo integration is a technique for numerical integration using random numbers and a a particular Monte Carlo method numerically computes the Riemann integral. Whereas other algorithms usually evaluate the integrand at a regular grid, Monte Carlo randomly chooses points at which the integrand is evaluated. This method is particularly useful for higher-dimensional integrals. There are different methods to perform a Monte Carlo integration, such as uniform sampling, stratified sampling, and importance sampling. In this chapter we describe a certain technique for numerical calculation of infinite-dimensional integrals by using methods of the theory of uniform distribution modulo (u.d.mod) 1. Development of this theory for one-dimensional Riemann integrals was begun by Hermann Weyl’s [W] celebrated theorem.
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