  Let X_1,X_2, . . . be a sequence of i.i.d. mean zero random variables and let
S_n the sum of the first n random variables. We show that whenever lim sup_n
|S_n|/c_n is finite with probability one and the normalizing sequence {c_n} is
sufficiently regular, the corresponding normalized partial sum process sequence
is relatively compact in C[0, 1] with canonical cluster set. Combining this
result with some LIL type results in the infinite variance case, we obtain
Strassen type results in this setting.
