“…ε k j t (ω)) → EF (Y 0 t (ω))(39)for some j → ∞ and some random element Y 0 t in C [0,T ] (R). We then understand (39) is just saying that Y ε t is weakly-compact under P. We will then make use of Lemma 5.1 in[29]. In fact, Lemma 5.1 in[29] indicates that in order to show weak-compactness of the family of sample paths in Y ε t in C [0,t] (R) under the measure P, it suffices to show, for each δ > 0, weak-compactness of the family of sample pathsY ε,δ t , where Y ε,δ t = Y ε t for σ k−1 ≤ t ≤ τ k , k = 1, 2, ..., N and Y ε,δ t = δ τ k − t τ k − σ k + 2δ t − σ k τ k − σ kfor τ k ≤ t ≤ σ k .…”