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A FUNCTIONAL LIMIT THEOREM FOR RANDOM WALK CONDITIONED TO STAY NON-NEGATIVE

A FUNCTIONAL LIMIT THEOREM FOR RANDOM WALK CONDITIONED TO STAY NON-NEGATIVE

In this paper we consider an aperiodic integer-valued random walk S and a process S* that is a harmonic transform of S killed when it first enters the negative half; informally, S* is ā€˜S conditioned to stay non-negativeā€™. If S is in the domain of attraction of the standard normal ā€¦