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Then, exchange the integral order and let x = m i γ i /S i, we can further obtain Pr (γ i < γth) as (11).

Secondly, from (I(1)>0) we further obtain the result that (R(1)>0).

Using the decomposition of a geometric series of radius α i z k, we further obtain ∑ k = 0 N p bN u - 1 f ( kbN u + i ) = ∑ k = 0 N p bN u - 1 ∑ ℓ = 0 L h - 1 α i z k ℓ. and, inverting the two sums, we have ∑ k = 0 N p bN u - 1 f ( kbN u + i ) = ∑ ℓ = 0 L h - 1 α i ℓ ∑ k = 0 N p bN u - 1 z ℓ k = N p bN u + ∑ ℓ = 1 L h - 1 ∑ k = 0 N p bN u - 1 α i ℓ ( z ℓ ) k. (38).

From the first equation of (11), we further obtain D ( Λ + δ δ + d ∑ i = 1 m γ i y i ) = d + ∑ i = 1 m β i y i. Substituting (12) into this equality, we further have.

We further obtain an associated Ito formula (see Theorem 8.1).

Then we further obtain.

We can further obtain another two insights.

By Proposition 2.2, we further obtain that (4.5).

By applying Theorem 2, we further obtain the following result.

In this part, we are going to further obtain average EE and average SE.

Applying the Cauchy-Schwartz inequality on the RHS of (10), we further obtain (11).