The YUIMA Project is an open source and collaborative effort aimed at developing the R package yuima for simulation and inference of stochastic differential equations. In the yuima package stochastic differential equations can be of very abstract type, multidimensional, driven by Wiener process or fractional Brownian motion with general Hurst parameter, with or without jumps specified as Lévy noise. The yuima package is intended to offer the basic infrastructure on which complex models and inference procedures can be built on. This paper explains the design of the yuima package and provides some examples of applications.

We will focus on estimating the integrated covariance of two diffusion processes observed in a nonsynchronous manner. The observation data is contaminated by some noise, which is possibly correlated with the returns of the diffusion processes, while the sampling times also possibly depend on the observed processes. This situation is much more realistic than those in which both of the noise and the sampling times are independent of the diffusion processes. In a high-frequency setting, we consider a modified version of the pre-averaged HayashiYoshida estimator, and we show that such a kind of estimators has the consistency and the asymptotic mixed normality, and attains the optimal rate of convergence.

This paper establishes an upper bound for the Kolmogorov distance between the maximum of a highdimensional vector of smooth Wiener functionals and the maximum of a Gaussian random vector. As a special case, we show that the maximum of multiple Wiener-Itô integrals with common orders is well-approximated by its Gaussian analog in terms of the Kolmogorov distance if their covariance matrices are close to each other and the maximum of the fourth cumulants of the multiple Wiener-Itô integrals is close to zero. This may be viewed as a new kind of fourth moment phenomenon, which has attracted considerable attention in the recent studies of probability. This type of Gaussian approximation result has many potential applications to statistics.To illustrate this point, we present two statistical applications in high-frequency financial econometrics: One is the hypothesis testing problem for the absence of lead-lag effects and the other is the construction of uniform confidence bands for spot volatility.Let m * be an integer such that |ρ m * |Σ(θ m * ) = max 1≤m≤M |ρ m |Σ(θ m ). By assumption [A4], for each n ∈ N there is a number ϑ n ∈ G n such that |ϑ n − θ m * | ≤ υ n . Now noting (B.5), we havefor sufficiently large n. Let us denote by ⊖ the symmetric difference between two sets. Then we have

An increased influx of extracellular Zn into neurons is a cause of cognitive decline. The influx of extracellular Zn into dentate granule cells was compared between young and middle-aged rats because of vulnerability of the dentate gyrus to aging. The influx of extracellular Zn into dentate granule cells was increased in middle-aged rats after injection of AMPA and high K into the dentate gyrus, but not in young rats. Simultaneously, high K-induced attenuation of LTP was observed in middle-aged rats, but not in young rats. The attenuation was rescued by co-injection of CaEDTA, an extracellular Zn chelator. Intracellular Zn in dentate granule cells was also increased in middle-aged slices with high K, in which the increase in extracellular Zn was the same as young slices with high K, suggesting that ability of extracellular Zn influx into dentate granule cells is greater in middle-aged rats. Furthermore, extracellular zinc concentration in the hippocampus was increased age-dependently. The present study suggests that the influx of extracellular Zn into dentate granule cells is more readily increased in middle-aged rats and that its increase is a cause of age-related attenuation of LTP in the dentate gyrus.

We propose a novel framework to investigate lead-lag relationships between two financial assets. Our framework bridges a gap between continuous-time modeling based on Brownian motion and the existing wavelet methods for lead-lag analysis based on discrete-time models and enables us to analyze the multi-scale structure of lead-lag effects. We also present a statistical methodology for the scale-by-scale analysis of lead-lag effects in the proposed framework and develop an asymptotic theory applicable to a situation including stochastic volatilities and irregular sampling. Finally, we report several numerical experiments to demonstrate how our framework works in practice. J for some universal constant c 4 > 0, hence we obtainWe rewrite the target quantity as, we obtain (35) by the dominated convergence theorem once we prove Ξ J (i 1 , i 2 ) → 0 for any fixed i 1 , i 2 . By Lemma 7 we haveWe can take sufficiently large r such that 2/r < 1 − κ. Then we haveJ )|X]| r ] = O τ 1−2/r J L 2 log 2 τ J r/2 = o(1) by Lemma 12. This yields the desired result. N τ J by the triangle and Schwarz inequalities. Therefore, the Markov inequality yields P max l∈L + J |I J (l)| > ε ≤ ε −1 l∈L + J I J (l) 2 2 N 2 τ J for any ε > 0, hence max l∈L + J |I J (l)| → p 0.Noting that L 2 τ J → 0, we can prove max l∈L + J |II J (l)| → p 0 in an analogous manner to the above.Next we prove max l∈L + J |III J (l)| → p 0. For any k ∈ I m,N (i) we haveWe can prove max l∈L + J |IV J (l)| → p 0 in an analogous manner.Now we prove max l∈L + J |V J (l)| → p 0. By Lemma 14 and the boundedness of σ 1 and σ 2 , we haveψ 1 → 0 by assumptions. This especially implies that max l∈L + J |V J (l)| → p 0. Finally, by Lemmas 4(b) and 8 we have max l∈L + J |VI J (l)| = o p (M J · τ −1 J τ m · τ J ). Since M J = O(τ −1 m ), we obtain max l∈L + J |VI J (l)| → p 0. This completes the proof. Completion of the proof of Theorem 2We need the following auxiliary result:Lemma 15. Λ −j D(λ)Π(λ)e

This paper presents a central limit theorem for a pre-averaged version of the realized covariance estimator for the quadratic covariation of a discretely observed semimartingale with noise. The semimartingale possibly has jumps, while the observation times show irregularity, nonsynchronicity, and some dependence on the observed process. It is shown that the observation times' effect on the asymptotic distribution of the estimator is only through two characteristics: the observation frequency and the covariance structure of the noise. This is completely different from the case of the realized covariance in a pure semimartingale setting.

The role of metallothioneins (MTs) in cognitive decline associated with intracellular Zn dysregulation remains unclear. Here, we report that hippocampal MT induction defends cognitive decline, which was induced by amyloid β (Aβ)-mediated excess Zn and functional Zn deficiency. Excess increase in intracellular Zn, which was induced by local injection of Aβ into the dentate granule cell layer, attenuated in vivo perforant pathway LTP, while the attenuation was rescued by preinjection of MT inducers into the same region. Intraperitoneal injection of dexamethasone, which increased hippocampal MT proteins and blocked Aβ-mediated Zn uptake, but not Aβ uptake, into dentate granule cells, also rescued Aβ-induced impairment of memory via attenuated LTP. The present study indicates that hippocampal MT induction blocks rapid excess increase in intracellular Zn in dentate granule cells, which originates in Zn released from Aβ, followed by rescuing Aβ-induced cognitive decline. Furthermore, LTP was vulnerable to Aβ in the aged dentate gyrus, consistent with enhanced Aβ-mediated Zn uptake into aged dentate granule cells, suggesting that Aβ-induced cognitive decline, which is caused by excess intracellular Zn, can more frequently occur along with aging. On the other hand, attenuated LTP under functional Zn deficiency in dentate granule cells was also rescued by MT induction. Hippocampal MT induction may rescue cognitive decline under lack of cellular transient changes in functional Zn concentration, while its induction is an attractive defense strategy against Aβ-induced cognitive decline.

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