Measurement of subpicosecond optical waveforms using a resonator-based phase modulator

We propose a method for the measurement of periodic optical waveforms based on the use of an electrooptic phase modulator placed in an optical Fabry-Perot or ring resonator. Significant broadening of the modulation spectrum extends the recently developed method of periodic modulation for pulse characterization into femtosecond scales. We numerically demonstrate the characterization of a 300-fs optical pulse. We also present a technique based on the temporal fractional Talbot effect for restoration of the pulse phase profile. After fast linear processing, subpicosecond pulses will be observed on the screen of a real-time oscilloscope. This complete characterization of optical pulses is entirely linear and therefore highly sensitive and simple in implementation.     

Distributed strain measurement using a tellurite glass fiber with Brillouin optical correlation-domain reflectometry

A tellurite glass fiber with a high Brillouin gain was employed for distributed strain measurement with Brillouin optical correlation-domain reflectometry (BOCDR). First, the spatial resolution of BOCDR was evaluated using the tellurite fiber. With the high Brillouin gain of the fiber, it was confirmed clearly in the experiment that the spatial resolution is limited by the Rayleigh scattering-induced noise. Then, the dependence of the Brillouin frequency shift (BFS) on strain in the tellurite fiber was investigated, showing a negative dependence with a coefficient of −0.023 MHz/με. Using this tellurite fiber, the distribution of the BFS around a 1-cm strain-applied section was successfully measured with BOCDR of a nominal spatial resolution of 6 mm.     

Interpolation algorithm for recovering the missing phase values in 3D measurement

In the three-dimensional (3D) phase measurement, some marks are usually adhered to the object in order to make the 3D registration process faster and easier. As covered with marks, local phase data are missing and have to be interpolated later. Considering the phase distribution nearby the marks, a gradient estimate (GE) interpolation algorithm is provided here. This algorithm recovers one pixel's missing phase value with the average of the estimated values which is calculated by gradients in eight directions nearby. Since this algorithm is a local processing, the missing phase values should be interpolated from the edge of the marks to the center. In the computer simulation and the practical experiment, compared with the same-size neighborhood mean (NM) algorithm and the Gerchberg-Saxton (GS) algorithm, this new algorithm achieves very good fit results with the least time. So it can be used as a practical tool for automatic missing phase interpolation.     

Adaptive Penalized Weighted Least Absolute Deviations Estimation for the Accelerated Failure Time Model

The accelerated failure time model always offers a valuable complement to the traditional Cox proportional hazards model due to its direct and meaningful interpretation. We propose a variable selection method in the context of the accelerated failure time model for survival data, which can simultaneously complete variable selection and parameter estimation. Meanwhile, the proposed method can deal with the potential outliers in survival times as well as heteroscedastic model errors, which are frequently encountered in practice. Specifically, utilizing the general nonconvex penalty, we propose the adaptive penalized weighted least absolute deviation estimator for the accelerated failure time model. Under some regularity conditions, we show that the proposed method yields consistent estimator and possesses the oracle property. In addition, we propose a new algorithm to compute the estimate in the high dimensional settings, and evaluate the practical utility of the proposed method through extensive simulation studies and two real examples.     

Local Functional Limit Theorems of Increments for Brownian Motion

In this paper, we present a local Csrg–Révész type functional limit theorem for increments of Brownian motion and give its convergence rate. The results also extend the functional forms of Lévy's modulus of continuity for Brownian motion.     

On a semilinear double fractional heat equation driven by fractional Brownian sheet

In this paper, we consider the stochastic heat equation of the form $$\frac{\partial u}{\partial t}=(\Delta_\alpha+\Delta_\beta)u+\frac{\partial f}{\partial x}(t,x,u)+\frac{\partial^2W}{\partial t\partial x},$$ where $1<\beta<\alpha< 2$, $W(t,x)$ is a fractional Brownian sheet, $\Delta_\theta:=-(-\Delta)^{\theta/2}$ denotes the fractional Lapalacian operator and $f:[0,T]\times \mathbb{R}\times \mathbb{R}\rightarrow\mathbb{R}$ is a nonlinear measurable function. We introduce the existence, uniqueness and H\"older regularity of the solution. As a related question, we consider also a large deviation principle associated with the above equation with a small perturbation via an equivalence relationship between Laplace principle and large deviation principle.     

Rough paths analysis of general Banach space-valued Wiener processes

In this article, we carry out a rough paths analysis for Banach space-valued Wiener processes. We show that most of the features of the classical Wiener process pertain to its rough path analog. To be more precise, the enhanced process has the same scaling properties and it satisfies a Fernique type theorem, a support theorem and a large deviation principle in the same Hölder topologies as the classical Wiener process does. Moreover, the canonical rough paths of finite dimensional approximating Wiener processes converge to the enhanced Wiener process. Finally, a new criterion for the existence of the enhanced Wiener process is provided which is based on compact embeddings. This criterion is particularly handy when analyzing Kunita flows by means of rough paths analysis which is the topic of a forthcoming article.     

Brown运动增量在H(o)lder范数下关于(r,p)-容度的泛函极限定理

利用Brown运动在H\"older 范数下关于$(r,p)$-容度的大偏差,证明了Brown运动增量在H\"older范数下关于$(r,p)$-容度的泛函极限定理.     

可列齐次马氏链熵率的指数收敛速度

运用Markov不等式和期望、强遍历、δ系数的性质,利用Chang提出的研究指数收敛速度的方法,在给出5个引理的基础上,研究了初始状态给定的一类可列齐次马氏链熵率的收敛速度,推广了Chang的结果.     

√2x^2-√2n-1的近似正态性及多总体标准差的齐性检验

计算了随机变量√2x^2的数学期望和方差,比较分析了随机变量√2x^2-√2n与√2x^2-√2n-1的近似分布的相同和不同之处,并且利用√2x^2的近似分布的正态性,建立了多总体标准差的检验法．