According to the UML 2.5.1 specification, a Stereotype must be owned (directly or indirectly) by a Profile, or by a Package which is contained in the Profile (diagram from p. 295):

However, on page 301-302 under section 12.3.3.4 Stereotypes, there is this sentence on p. 302:

“The type of a composite aggregation Stereotype Property cannot be a Stereotype (since Stereotypes are owned by their Extensions) or a metaclass (since instances of metaclasses are owned by other instances of metaclasses)…”

I do not understand how a Stereotype can be owned by an Extension. Is this a mistake? Probably “Profiles” should be substituted for “Extensions” here?