Non-finite clauses and PRO

[mallu]

PRO is supposed to occupy subject position of non-finite clauses. Isn't it?
But see the following sentences.
1John preferred [eating a bagel]
2John prefer [ travelling alone]
Are the bracketted strings non-finite clauses like
3 John prefer to travel alone
Hope someone would come out to help me

[Daniel]

It entirely depends on your theoretical analysis.

Assuming that you believe "to travel" contains PRO, then I see two options:

1. Yes, these gerunds have PRO. I've seen arguments like that, and it especially makes sense when they're more adverbial:
PRO looking at the sunset, John was happy.

2. These are nouns, so they have no subject.

One way to check this is to see whether a reflexive that agrees with the subject can be found in the embedded(?) clause:
John preferred paying for himself.

When that is allowed, it seems that there must be a PRO there, under that theory.