22 Simulation of Brownian motion
This chapter presents a concise introduction to simulation, in particular focusing on the normal distribution and Brownian motion.
22.1 Introduction
Recall that for iid random variables X1, . . . Xn with a common distribution F for any ω ∈ Ω the tuple (X1 (ω), . . . , Xn(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 (ϰ1, . . . , ϰn) 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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