  For a strictly stationary sequence of nonnegative regularly varying random
variables $(X_{n})$ we study functional weak convergence of partial maxima
processes $M_{n}(t) = \bigvee_{i=1}^{\lfloor nt \rfloor}X_{i},\,t \in [0,1]$ in
the space $D[0,1]$ with the Skorohod $J_{1}$ topology. Under the strong mixing
condition, we give sufficient conditions for such convergence when clustering
of large values do not occur. We apply this result to stochastic volatility
processes. Further we give conditions under which the regular variation
property is a necessary condition for $J_{1}$ and $M_{1}$ functional
convergences in the case of weak dependence. We also prove that strong mixing
implies the so-called Condition $\mathcal{A}(a_{n})$ with the time component.
