No abstract

The coefficients in a general second order linear stochastic partial differential equation (SPDE) are estimated from multiple spatially localised measurements. Assuming that the spatial resolution tends to zero and the number of measurements is non-decreasing, the rate of convergence for each coefficient depends on the order of the parametrised differential operator and is faster for higher order coefficients. Based on an explicit analysis of the reproducing kernel Hilbert space of a general stochastic evolution equation, a Gaussian lower bound scheme is introduced. As a result, minimax optimality of the rates as well as sufficient and necessary conditions for consistent estimation are established.

We searched for the presence of 26 Al in deep-sea sediments as a signature of supernova influx. Our data show an exponential dependence of 26 Al with the sample age that is fully compatible with radioactive decay of terrigenic 26 Al. The same set of samples demonstrated a clear supernova 60 Fe signal between 1.7 and 3.2 Myr ago. Combining our 26 Al data with the recently reported 60 Fe data results in a lower limit of 0.18 +0.15 −0.08 for the local interstellar 60 Fe/ 26 Al isotope ratio. It compares to most of the ratios deduced from nucleosynthesis models and is within the range of the observed average galactic 60 Fe/ 26 Al flux ratio of (0.15±0.05). The radionuclides 26 Al (t 1/2 =0.717±0.017 Myr [1]) 1 and 60 Fe (t 1/2 =2.61±0.04 Myr [2-4]) are key isotopes for 2 understanding nucleosynthesis in our galaxy. Both were 3 present in the early solar system, as evidenced by an ex-4 cess of their decay-products in meteorites [5, 6]. Today, 5 the decay of live 26 Al and 60 Fe is observed in the interstel-6 lar medium (ISM) through their associated characteristic 7 γ-rays [7, 8]. 8 Significant amounts (3-10 %) of 26 Al and 60 Fe are 9 freshly synthesized and ejected into the ISM by (su-10 per) asymptotic giant branch-(S)AGB-stars in the 11 mass range of ∼5-9 M ⊙ [9, 10]. However, the major frac-12 tion is thought to be released by massive stars (9 M ⊙) 13 that explode as core-collapse supernovae (CCSNe) [11-14 13]. Electron-capture (EC)SNe (∼7-11 M ⊙) produce 15 60 Fe, but negligible 26 Al during explosive nucleosynthesis 16 [10, 14]. Additionally, stellar winds of Wolf-Rayet (WR) 17 stars with masses >40 M ⊙ , which also end their lives as 18 SNe, have been proposed as major sources for the galac-19 tic 26 Al inventory [15, 16], while they are not believed to 20 contribute significant amounts of 60 Fe [13, 17]. Hence, 21 the observed ISM distribution of 26 Al and 60 Fe combines 22 a mixture of different stellar sources, with a galactic av-23 eraged 60 Fe/ 26 Al γ-ray flux ratio of (0.15±0.05) [8]. 24 Freshly produced radionuclides from supernova (SN) 25 explosions can be transported over large interstellar dis-26 tances. Material ejected from nearby SNe can enter our 27 solar system and cross the Earth's orbit, potentially leav-28 ing traces of the ejecta in terrestrial archives [18, 19]. 29 Indeed, the radionuclide 60 Fe has been identified in ter-30 restrial [20-24] and lunar samples [25]. The detection of 31 SN-associated 60 Fe deposited about 2-3 Myr ago provides 32 an opportunity to determine the specific SN-associated 33 26 Al/ 60 Fe ratio, disentangling it from the observed galac-34 tic average ratio. 35 Here, we present for the first time a detailed 26 Al time 36 profile and combine this data with the previously mea-37 sured SN-associated 60 Fe data from the same deep-sea 38 sediments [22] to derive the 60 Fe/ 26 Al ratio associated 39 with the recent and local SN events. First, we esti-40 mate whether SN-associated 26 Al is within the detection 41 limit of accelerator mass spectrometry (AMS) using an 42 60 ...

We consider noisy non-synchronous discrete observations of a continuous semimartingale with random volatility. Functional stable central limit theorems are established under high-frequency asymptotics in three setups: one-dimensional for the spectral estimator of integrated volatility, from twodimensional asynchronous observations for a bivariate spectral covolatility estimator and multivariate for a local method of moments. The results demonstrate that local adaptivity and smoothing noise dilution in the Fourier domain facilitate substantial efficiency gains compared to previous approaches. In particular, the derived asymptotic variances coincide with the benchmarks of semiparametric Cramér-Rao lower bounds and the considered estimators are thus asymptotically efficient in idealized subexperiments. Feasible central limit theorems allowing for confidence bounds are provided.