ABSTRACT
In this chapter, we discuss the numerical evaluation of E ( X ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315368757/e88f714d-2ba9-44cc-aeea-7a975525e77e/content/eq263.tif"/> by the empirical mean X ¯ M : = 1 M ∑ m = 1 M X m https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315368757/e88f714d-2ba9-44cc-aeea-7a975525e77e/content/eq264.tif"/> https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315368757/e88f714d-2ba9-44cc-aeea-7a975525e77e/content/eq75.tif"/> where (X m) m ≥ 1 are independent simulations having the same distribution as X. This is the basic principle of Monte-Carlo methods for the calculation of expectation.
