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THEOREM 1.1.– Let conditions 1.3 and 1.1 (1.2) for the continuous-time (for the discrete-time) case be fulfilled. If ρ ≥ 1, then

[1.9]

PROOF.– Consider the embedded process Qn = Q(Tn) and denote

Define the auxiliary sequence recursion

Because of the equality and condition 1.3 we get the stochastic inequality It is well known (Feller 1971) that

and in distribution

For ρ ≥ 1, the sequence is a random walk with a non-negative drift. Hence, except when (c is a constant), (w.p.1) (Feller 1971) that completes the proof. ■