t+1 Sample Clauses

t+1 t+1 information. The update is calculated as follows: t+1 t+1 Q(si , ai ) = (1 −α)Q(si, ai) + α(ri + γ max Q(si , ai ). (3.11) a

t+1 t+1 The update equation is given as follows t+1 t+1 Q(si , ai ) = (1 −α)Q(si, ai) + α(ri + γ max Q(si , ai ). (4.3) a

t+1. T t+1 t+1 2 max(α, µ) t

t+1. Suppose that a rate tuple (RS, RJ , RL) is achievable, im- plying that there exists a pair of encoder and decoder such that all the requirements in Definition 2 are satisfied for small enough δ > 0 and block length n n0 (n0 1). Let auxiliary RVs Ut = (J, S, Y n , Zt−1) and Vt = (J, Y n , Zt−1). where (d) is due to the Markov chain Zn (X˜n, S) J − − t+1 − − and S is independent of other RVs, (e) is due to the Markov chain X˜t (X˜t−1, J, S, Zn) Y n , and (f) follows because conditioning does not increase entropy. Analysis of Privacy-Leakage Rate: We can develop the right- hand side of (6) as n(RL + δ) ≥ I(Xn; J, Zn) Under this settings, it is easy to verify that the Markov chain Vt − Ut − X˜t − Xt − (Yt, Zt) is satisfied. Analysis of Secret-key Rate: By a similar argument of [13, eq. (40)], from (7), the secret-key rate can be bounded by n(RS − δ) ≤ log MS = H(S) n + δ) Σ = I(Xn; J, S, Zn) − I(Xn; S|J, Zn) n n ≥ I(X ; J, S, Z ) − H(S) = I(Xn; J, S|Zn) + nI(X; Z) − H(S) = I(Xn; J|S, Zn) + nI(X; Z) − H(S) n Σ(h) ≥ I(Xt; Ut|Zt) + nI(X; Z) − H(S) (g) Σ ≤

t+1 t=1 where s is the frequency, which is twelve here, and Σs h2,t = 1 while Σs h1,t = 3 (the three-month aggregates ending in April and May include both March and April; hence two months for which ht is equal to one). In the US, businesses can see their turnover fluctuate considerably round the seven days preceding Easter and it is usual to set Ht = 7. However, Xxxx and Xxxxx (2017) suggest using a specific Easter period for the UK. Their results show that it is better to account for the period Good Friday to Easter Monday, the entire bank holiday period, or from Monday before Easter Sunday to Friday following it. Here the former is chosen and Ht is set to four. The trading days effects are usually insignificant with quarterly data because the varying number of trading days in a month partially averages out over three months (X-13ARIMA-SEATS reference manual, US Census Bureau).‌

t+1 t+1 t+1 t+1 Vt+1 Vt .o . a2 = 4 + δVt+1 . .o . . • If V . .o ≥ V .o , V . ≥ V . , and . .o .