Fractal Activity Time Models for Risky Asset with Dependence and Generalized Hyperbolic Distributions

Risky asset models with the dependence through fractal activity time are described. The construction of the fractal activity time is implemented via superpositions of Ornstein-Uhlenbeck type processes driven by Lévy noise. The model features both tractable dependence structure and desired marginal distributions of the returns from the generalized hyperbolic class: the Variance Gamma and normal inverse Gaussian. These distributions provide good fit to real financial data. Pricing formulae for the proposed models are derived.     

Impulsive Noise Driven One-Dimensional Higher-Order Fractional Partial Differential Equations

We are going to study a kind of stochastic fractional partial differential equation driven by an impulsive noise, which is singular not only in time but also in space. We first study the existence and uniqueness of the solution and then investigate the regularity of the solution in its spatial variable which depends on the order of the fractional operator, and deeply relies on the precise analysis of the kernel generated by our operator. In addition, we also discuss the stochastic flow property of the solutions.     

A Multivariate Regime-Switching Mean Reverting Process and Its Application to the Valuation of Credit Risk

In this article, we study the counterparty risk on a credit default swap (CDS) and the valuation of a first-to-default basket swap on three underlyings under a common shock model with regime-switching intensities. We assume that the defaults of all the names are driven by some shock events, whose arrivals are governed by a multivariate regime-switching shot noise process. Based on some expressions for the joint Laplace transform of the regime-switching shot noise processes, we give explicit formulas for the spread of the CDS contract with and without counterparty risk and the spread of the first-to-default basket swap on the three underlyings.     

Terminal-Dependent Statistical Inferences for FBSDE

Backward stochastic differential equation (BSDE) has been well studied and widely applied in mathematical finance. The main difference from the original stochastic differential equation (OSDE) is that the BSDE is designed to depend on a terminal condition, which plays key roles in certain financial and ecological circumstances. However, to the best of our knowledge, the terminal-dependent statistical inference for such model has not been explored in the existing literature. This article proposes two terminal-dependent estimation methods via terminal control variable the integral form models of forward-backward stochastic differential equation (FBSDE). We take these measures because the resulting models contain terminal condition as model variable, and therefore, the corresponding estimators inherit the terminal-dependent characteristic. In this article, the FBSDE is first rewritten as regression versions and then two semi-parametric estimation approaches are proposed. Because of the control variable and integral form, our regression versions are more complex than the classical ones, and the inference methods are somewhat different from which designed for the OSDE. Even so, the statistical properties of the terminal-dependent methods are similar to the classical ones. Simulations are conducted to demonstrate finite sample behaviors.     

A Large Deviation Principle of Retarded Ornstein-Uhlenbeck Processes Driven by Lévy Noise

In this article, we develop a large deviation principle (LDP) for a class of retarded Ornstein-Uhlenbeck processes driven by Lévy processes. We first present a LDP result for time delay systems driven by cylindrical Wiener processes based on the large deviations of Gaussian processes. By using a contraction technique and passing on a finite-dimensional approximation, an LDP is obtained for stochastic time delay evolution equations driven by additive Lévy noise, whose solutions are generally not Lévy processes any more.     

Thermal noise as a spectroscopic tool to determine transport properties

The utilization of thermal fluctuations or Johnson/Nyquist noise as a spectroscopic method to determine transport properties in conductors or semiconductors is developed. The autocorrelation function is obtained from power spectral density measurements thus enabling electronic transport property calculation through the Green–Kubo formalism. This experimental approach is distinct from traditional numerical methods such as molecular dynamics simulations, which have been used to extract the autocorrelation function and directly related physics only. This work reports multi-transport property measurements consisting of the electronic relaxation time, resistivity, mobility, diffusion coefficient, electronic contribution to thermal conductivity and Lorenz number from experimental data. Double validation of the experiment was accomplished through the use of a standard reference material and a standard measurement method, i.e. four-probe collinear resistivity technique. Thermal noise measurements resulted in a 1.1 and 5% agreement with the reference material and four-probe values, respectively. Additional measurements were also taken on nanoscale Au and Cu thin films. Specifically, the validated spectroscopic methodology was applied to 30 nm Au and Cu thin films to obtain transport property data that was again compared to four-probe resistivity measurements. Comparative analysis of the resistivity data showed agreement within 13.6 and 4.8% for the Au and Cu samples, respectively, thus lending further credibility to the experimental method and theory.     

基于CDMA的布拉格光纤光栅传感系统的仿真分析

讨论了光纤光栅传感系统中常用的复用技术及其限制,阐述了利用CDMA技术实现光纤布拉格光栅阵列波长解调的复用方式,对系统的原理和性能进行了理论分析。在此基础上通过MATLAB做了基于CDMA的光纤光栅传感仿真分析,仿真结果表明该方法能区分反射波长重叠的光栅,从而提高FBG网络复用的频带利用率。     

Spin-dependent negative differential conductance in transport through single-molecule magnets

Transport properties are theoretically studied through an anisotropy single-molecule magnet symmetrically connected to two identical ferromagnetic leads. It is found that even though in parallel configuration of leads’ magnetizations, the total current still greatly depends on the spin polarization of leads at certain particular bias region, and thus for large polarization a prominent negative differential conductance (NDC) emerges. This originates from the joint effect of single-direction transitions and spin polarization, which removes the symmetry between spin-up and spin-down transitions. The present mechanism of NDC is remarkably different from the previously reported mechanisms. To clarify the physics of the NDC, we further monitored the shot noise spectroscopy and found that the appearance of the NDC is accompanied by the rapid decrease of Fano factor.     

The mean first passage time of a three-level atomic optical bistable system subjected to noise

The transient properties of a three-level atomic optical bistable system in the presence of multiplicative and additive noises are investigated. The explicit expressions of the mean first-passage time (MFPT) of the transition from the high intracavity intensity state to the low one are obtained by numerical computations. The impacts of the intensities of the multiplicative noise D M and the additive noise D A , the intensity of correlation between two noises λ , and the intensity of the incident light y on the MFPT are discussed, respectively. Our results show: (i) for the case of no correlation between two noises (λ = 0.0), the increase in D M and D A can lead to an increase in the probability of the transition to the low intracavity intensity state, while the increase in y can lead to a retardation of the transition; and (ii) for the case of correlation between two noises (λ = 0.0), the increase in λ can cause an increase in the probability of the transition, and the increase in D A can cause a retardation of the transition firstly and then an increase in the probability of the transition, i.e., the noise-enhanced stability is observed for the case of correlation between two noises.