Hi:

Think about the primary task of a BA in an any environment - Agile or Waterfall.  The primary responsibility of a BA is (or should be)  to come up with the bigger picture. 

With Waterfall,  the top most BA goal is to come up with bigger picture of the needed processes and their essential interrelationships.  (This can be done with what are called Essential Data Flow Diagrams.)   This is also the same top most goal for BA's in Agile projects.  Remember, that while Agile is about minimal documentation,  it is also about quality documentation:  It is about capturing the essentials, and only the essentials.

So, you see BA wise there really is no real difference.  The confusion comes into being because most people equate  bad Waterfall with Waterfall in general.  Successful Waterfall has always been about being minimal.   That is the way I lead projects going back to the early 80's:  A few higher level DFD's, some Entity Relationship Diagrams (ERDs), and maybe some screen shots;  that is all that is needed to really get things going. 

A ways back, I  had on-line conversation with noted Agile book author and Best Practices blog leader with CIO magazine, Michael Hugos.  He told me that such is how he, in the hear and now, leads and espouses Agile.

Tony