Monte Carlo Methods

This chapter studies Monte Carlo and quasi-Monte Carlo methods for integration, optimization, and probability and expected value estimation. The Monte Carlo method has been widely used for simulations of various physical and mathematical systems and has a very long history that began in 1949 with the seminal paper of Metropolis and Ulam. The name Monte Carlo probably originated from the famous casino in Monaco and reflects the random and repetitive nature of the process, which is similar to gambling in casinos. The quasi-Monte Carlo method is more recent and may be regarded as a deterministic version of Monte Carlo.

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