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(p.239)
Weak Convergence of Probability Measures on R^{p} and C[0,1]

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(p.239)
Weak Convergence of Probability Measures on R^{p} and C[0,1]

The purpose of this appendix is to explain the concept of weak convergence on C[0,1], the space of continuous functions on the unit interval [0,1]. It explains what is behind the formulae involving Brownian motion and stochastic integrals, which appear in the discussion of the limit distributions in cointegration theory. We discuss the existence of stochastic processes like Brownian motion, and find distributions of suitable functionals of Brownian motion using the continuous mapping theorem.

*Keywords:*
Brownian motion, continuous mapping theorem, stochastic integral, weak convergence

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