This chapter presents a concise introduction to simulation, in particular focusing on the normal distribution and Brownian motion.

Recall that for iid random variables X_{1}, . . . X_{n} with a common distribution F for any ω ∈ Ω the tuple (X_{1} (ω), . . . , X_{n}(ω)) is called a (true) sample of F. In simulations the following notion of a sample is commonly used.

22.1 Definition. A tuple of values (ϰ_{1}, . . . , ϰ_{n}) which is indistinguishable from a true sample of F by statistical inference is called a sample of F. An element of such a tuple is called a sample value of F, and it is denoted by

Note that the statistical inference has to ensure both the distributional properties and ...

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