10.1 Random vector

A random vector is a list of random variables, measurable in a proper way.

10.2 Joint laws and marginals

The joint law of two or more random variables is a law of a random vector. 

10.3 Multivariate densities

If a random vector admits a probability density function, then so do its coordinate variables. The converse is not true in general.

10.4 Laws of independence

The joint law of mutually independent random variables is a product measure.

10.5 Densities of independent random variables

Densities of independent random variables factorise almost everywhere.


10.6 Expectations of independent products

Under independence, the expectation of a product equals a product of expectations. 


Alternative reading material

  • [Jacod & Protter, Chapters 10 and 12]
  • [Williams, Chapter 8]

Last modified: Thursday, 11 February 2021, 1:48 AM