Semiparametric estimation for a class of time-inhomogenous diffusion processes

Copyright @ 2009 Institute of Statistical Science, Academia SinicaWe develop two likelihood-based approaches to semiparametrically estimate a class of time-inhomogeneous diffusion processes: log penalized splines (P-splines) and the local log-linear method. Positive volatility is naturally embedded and this positivity is not guaranteed in most existing diffusion models. We investigate different smoothing parameter selections. Separate bandwidths are used for drift and volatility estimation. In the log P-splines approach, different smoothness for different time varying coefficients is feasible by assigning different penalty parameters. We also provide theorems for both approaches and report statistical inference results. Finally, we present a case study using the weekly three-month Treasury bill data from 1954 to 2004. We find that the log P-splines approach seems to capture the volatility dip in mid-1960s the best. We also present an application to calculate a financial market risk measure called Value at Risk (VaR) using statistical estimates from log P-splines

Detection of distinct power spectra in soft and hard X-ray bands in the hard state of GRS 1915+105

The well-known black hole X-ray binary GRS 1915+105 is a unique source in the sense that it cannot be classified within the standard picture of black hole binary states. In this work we study archival XMM-Newton observations taken between 2003 and 2004 of the \c{hi} variability class of GRS 1915+105, which corresponds to the hard state in the standard black hole X-ray binary state classification. The crucial point of our study is that by using XMM-Newton data we can access the variability below 3 keV, an energy range that is not covered with RXTE. We focus on the study of the power spectral shape in the soft and hard X-ray band, in light of our work done with Swift on MAXI J1659-152. In the hard band (above 2.5 keV) power density spectra consist of band-limited noise and quasi-periodic oscillations, corresponding to the power spectral shape seen in the hard or intermediate state, while in the soft band the averaged power density spectrum is consistent with a power-law noise, corresponding to the power spectral shape usually seen in the soft state. The coexisting of two different power spectral shapes in the soft and hard band, where the soft band power spectrum is dominated by a power-law noise, is consistent with MAXI J1659-152, and confirms the energy dependence of power spectral states. Our additional spectral analysis shows that the disc component does contribute to the soft band flux. These findings support that the observed black hole power spectral state depends on which spectral component we are looking at, which implies that power spectral analysis is probably a more sensitive method than spectral modeling to trace the emergence of the disc component in the hard or intermediate state.Comment: 9 pages, 5 figures, submitted to MNRA

Phonon decoherence of quantum entanglement: Robust and fragile states

We study the robustness and fragility of entanglement of open quantum systems in some exactly solvable models in which the decoherence is caused by a pure dephasing process. In particular, for the toy models presented in this paper, we identify two different time scales, one is responsible for local dephasing, while the other is for entanglement decay. For a class of fragile entangled states defined in this paper, we find that the entanglement of two qubits, as measured by concurrence, decays faster asymptotically than the quantum dephasing of an individual qubit.Comment: 11 pages, revtex, no figure

Coherent State Control of Non-Interacting Quantum Entanglement

We exploit a novel approximation scheme to obtain a new and compact formula for the parameters underlying coherent-state control of the evolution of a pair of entangled two-level systems. It is appropriate for long times and for relatively strong external quantum control via coherent state irradiation. We take account of both discrete-state and continuous-variable degrees of freedom. The formula predicts the relative heights of entanglement revivals and their timing and duration.Comment: Published in PRA, 10 pages, 7 figure