  Parabolic Higgs bundles can be described in terms of decorated swamps, which
we studied in a recent paper. This description induces a notion of stability of
parabolic Higgs bundles depending on a parameter, and we construct their moduli
space inside the moduli space of decorated swamps. We then introduce asymptotic
stability of decorated swamps in order to study the behavior of the stability
condition as one parameter approaches infinity. The main result is the
existence of a constant, such that stability with respect to parameters greater
than this constant is equivalent to asymptotic stability. This implies
boundedness of all decorated swamps which are semistable with respect to some
parameter. Finally, we recover the usual stability condition of parabolic Higgs
bundles as asymptotic stability.
