Parameter estimation and model testing for Markov processes via conditional characteristic functions

Markov processes are used in a wide range of disciplines, including finance. The transition densities of these processes are often unknown. However, the conditional characteristic functions are more likely to be available, especially for L\'{e}vy-driven processes. We propose an empirical likelihood approach, for both parameter estimation and model specification testing, based on the conditional characteristic function for processes with either continuous or discontinuous sample paths. Theoretical properties of the empirical likelihood estimator for parameters and a smoothed empirical likelihood ratio test for a parametric specification of the process are provided. Simulations and empirical case studies are carried out to confirm the effectiveness of the proposed estimator and test.Comment: Published in at http://dx.doi.org/10.3150/11-BEJ400 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Physical modeling and validation of porpoises' directional emission via hybrid metamaterials

© The Author(s), 2019. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Dong, E., Zhang, Y., Song, Z., Zhang, T., Cai, C., & Fang, N. X. Physical modeling and validation of porpoises' directional emission via hybrid metamaterials. National Science Review, 6(5), (2019): 921-928, doi:10.1093/nsr/nwz085.In wave physics and engineering, directional emission sets a fundamental limitation on conventional simple sources as their sizes should be sufficiently larger than their wavelength. Artificial metamaterial and animal biosonar both show potential in overcoming this limitation. Existing metamaterials arranged in periodic microstructures face great challenges in realizing complex and multiphase biosonar structures. Here, we proposed a physical directional emission model to bridge the gap between porpoises’ biosonar and artificial metamaterial. Inspired by the anatomical and physical properties of the porpoise's biosonar transmission system, we fabricated a hybrid metamaterial system composed of multiple composite structures. We validated that the hybrid metamaterial significantly increased directivity and main lobe energy over a broad bandwidth both numerically and experimentally. The device displayed efficiency in detecting underwater target and suppressing false target jamming. The metamaterial-based physical model may be helpful to achieve the physical mechanisms of porpoise biosonar detection and has diverse applications in underwater acoustic sensing, ultrasound scanning, and medical ultrasonography.E.D., Y.Z., Z.S., T.Z. and C.C. acknowledge the financial support in part by the National Key Research and Development Program of China (2018YFC1407504), the National Natural Science Foundation of China (41676023, 41276040 and 41422604). N.X.F. acknowledges the support from the MIT Energy Initiative grant. Z.S. thanks the China Scholarship Council for the financial support of his oversea study in Woods Hole Oceanographic Institution

Disorder and metal-insulator transitions in Weyl semimetals

The Weyl semimetal (WSM) is a newly proposed quantum state of matter. It has Weyl nodes in bulk excitations and Fermi arcs surface states. We study the effects of disorder and localization in WSMs and find three exotic phase transitions. (I) Two Weyl nodes near the Brillouin zone boundary can be annihilated pairwise by disorder scattering, resulting in the opening of a topologically nontrivial gap and a transition from a WSM to a three-dimensional (3D) quantum anomalous Hall state. (II) When the two Weyl nodes are well separated in momentum space, the emergent bulk extended states can give rise to a direct transition from a WSM to a 3D diffusive anomalous Hall metal. (III) Two Weyl nodes can emerge near the zone center when an insulating gap closes with increasing disorder, enabling a direct transition from a normal band insulator to a WSM. We determine the phase diagram by numerically computing the localization length and the Hall conductivity, and propose that the exotic phase transitions can be realized on a photonic lattice.Comment: 7 pages with appendix, 6 figure

Magneto-infrared spectroscopy of Landau levels and Zeeman splitting of three-dimensional massless Dirac Fermions in ZrTe5_5

We present a magneto-infrared spectroscopy study on a newly identified three-dimensional (3D) Dirac semimetal ZrTe$_5$. We observe clear transitions between Landau levels and their further splitting under magnetic field. Both the sequence of transitions and their field dependence follow quantitatively the relation expected for 3D \emph{massless} Dirac fermions. The measurement also reveals an exceptionally low magnetic field needed to drive the compound into its quantum limit, demonstrating that ZrTe$_5$ is an extremely clean system and ideal platform for studying 3D Dirac fermions. The splitting of the Landau levels provides a direct and bulk spectroscopic evidence that a relatively weak magnetic field can produce a sizeable Zeeman effect on the 3D Dirac fermions, which lifts the spin degeneracy of Landau levels. Our analysis indicates that the compound evolves from a Dirac semimetal into a topological line-node semimetal under current magnetic field configuration.Comment: Editors' Suggestio

Game-theoretic study of the dynamics of tourism supply chains for package holidays under quantity competition

2009-2010 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishe

Exponential asymptotics for time-space Hamiltonians

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