*2*

*Stochastic Convergence*

*This chapter provides a review of basic modes of convergence of sequences of stochastic vectors, in particular convergence in distribution and in probability.*

**2.1 Basic Theory**

A *random vector* in is a vector *X* = (*X*_{1},..., *X*_{k}) of real random variables.^{†} The *distribution function* of *X* is the map *x* *P*(*X* ≤ *x*).

A sequence of random vectors *X*_{n} is said to *converge in distribution* to a random vector *X* if

for every