Orbits in a stochastic Goodwin–Lotka–Volterra model

This paper examines the cycling behavior of a deterministic and a stochastic version of the economic interpretation of the Lotka–Volterra model, the Goodwin model. We provide a characterization of orbits in the deterministic highly non-linear model. We then study a stochastic version, with Brownian noise introduced via a heterogeneous productivity factor. Existence conditions for a solution to the system are provided. We prove that the system produces cycles around a unique equilibrium point in finite time for general volatility levels, using stochastic Lyapunov techniques for recurrent domains. Numerical insights are provided.     

Stochastic preference analysis in numerical preference relations

Numerical preference relations (NPRs) consisting of numerical judgments can be considered as a general form of the existing preference relations, such as multiplicative preference relations (MPRs), fuzzy preference relations (FPRs), interval MPRs (IV-MPRs) and interval FPRs (IV-FPRs). On the basis of NPRs, we develop a stochastic preference analysis (SPA) method to aid the decision makers (DMs) in decision making. The numerical judgments in NPRs can also be characterized by different probability distributions in accordance with practice. By exploring the judgment space of NPRs, SPA produces several outcomes including the rank acceptability index, the expected priority vector, the expected rank and the confidence factor. The outcomes are obtained by Monte Carlo simulation with at least 95% confidence degree. Based on the outcomes, the DMs can choose some of them which they find most useful to make reliable decisions.     

Relaxation dynamics in a stochastic bosonic Josephson junction

We consider a bosonic Josephson junction in the Bose-Hubbard two-mode approximation where some of the parameters are corrupted by physically meaningful noise processes and study the corresponding relaxation dynamics towards its equilibrium state. We show with numerical simulations that this model can essentially capture all the important features observed in a recent experiment regarding the relaxation dynamics in one-dimensional bosonic Josephson junctions, namely the damped oscillations of the population imbalance and the relative phase, as well as the large final coherence factor. We expect that this work will further motivate research about the origin of relaxation mechanism in these systems.     

Analysis and modeling of radiometric error caused by imaging blur in optical remote sensing systems

Imaging blur changes the digital output values of imaging systems. It leads to radiometric errors when the system is used for measurement. In this paper, we focus on the radiometric error due to imaging blur in remote sensing imaging systems. First, in accordance with the radiometric response calibration of imaging systems, we provide a theoretical analysis on the evaluation standard of radiometric errors caused by imaging blur. Then, we build a radiometric error model for imaging blur based on the natural stochastic fractal characteristics of remote sensing images. Finally, we verify the model by simulations and physical defocus experiments. The simulation results show that the modeling estimation result approaches to the simulation computation. The maximum difference of relative MSE (Mean Squared Error) between simulation computation and modeling estimation can achieve 1.6%. The physical experimental results show that the maximum difference of relative MSE between experimental results and modeling estimation is only 1.29% under experimental conditions. Simulations and experiments demonstrate that the proposed model is correct, which can be used to estimate the radiometric error caused by imaging blur in remote sensing images. This research is of great importance for radiometric measurement system evaluation and application.     

On uniform propagation of chaos

In this paper we obtain a time-uniform propagation estimate for a system of interacting diffusion processes. Using a well defined metric function h , our result guarantees a time-uniform estimate for the convergence of a class of interacting stochastic differential equations towards their mean field limit, under conditions that ensure that the decay associated to the internal dynamics term dominates the interaction and noise terms. Our result should have diverse applications, particularly in neuroscience, and allows for models more elaborate than the one of Wilson and Cowan. In particular, the internal dynamics need not be that of linear decay.     

基于傅立叶变换的SVJ模型的欧式期权定价

为了更加精确的计算期权价格,将结合随机波动和跳扩散模型(以下简称SVJ模型)以更好的描述期权标的资产价格过程,然而这样的价格过程无法得到概率密度函数的封闭形式,而只能得到包含特殊函数和无限求和的复杂的表达式.不过它们的特征函数都是封闭且是唯一的,因而可以通过它们的特征函数,并运用两种傅立叶变换的方法来求出期权价格.其中FFT算法计算的结果将与Monte Carlo模拟得出的结果进行比较,然后再将SVJ模型的计算结果和Black-Scholes模型进行比较.     

Well adjusted: Using expediting and cancelation to manage store replenishment inventory for a seasonal good

We consider an inventory problem that can be translated into a two-period newsvendor setting where the day prior to sales, the newsvendor places an initial preliminary order—a semi-binding forecast—with the publisher. At the beginning of the actual day of sales, the newsvendor has a better forecast for the day’s demand: based on knowing the actual content of the paper, he knows whether it will be a high-demand day due to breaking news or a low-demand day due to slow news. He then can revise the preliminary order quantity by expediting additional papers or canceling all or part of the order, but each of these activities has an associated cost.     

Tensor gauge field localization on a string-like defect

This work is devoted to the study of tensor gauge fields on a string-like defect in six dimensions. This model is very successful in localizing fields of various spins only by gravitational interaction. Due to problems of field localization in membrane models we are motivated to investigate if a string-like defect localizes the Kalb–Ramond field. In contrast to what happens in Randall–Sundrum and thick brane scenarios we find a localized zero mode without the addition of other fields in the bulk. Considering the local string defect we obtain analytical solutions for the massive modes. Also, we take the equations of motion in a supersymmetric quantum mechanics scenario in order to analyze the massive modes. The influence of the mass as well as the angular quantum number in the solutions is described. An additional analysis on the massive modes is performed by the Kaluza–Klein decomposition, which provides new details about the KK masses.     

Data envelopment analysis models of investment funds

This paper develops theory missing in the sizable literature that uses data envelopment analysis to construct return-risk ratios for investment funds. It explores the production possibility set of the investment funds to identify an appropriate form of returns to scale. It discusses what risk and return measures can justifiably be combined and how to deal with negative risks, and identifies suitable sets of measures. It identifies the problems of failing to deal with diversification and develops an iterative approximation procedure to deal with it. It identifies relationships between diversification, coherent measures of risk and stochastic dominance. It shows how the iterative procedure makes a practical difference using monthly returns of 30 hedge funds over the same time period. It discusses possible shortcomings of the procedure and offers directions for future research.     

The aliasing‐phenomenon in visual terms

In a recent paper it was shown that the aliasing phenomenon, which leads to a severe identification problem in the estimation of stochastic differential equations, can be overcome by using a polygonal (or higher) approximation for the time paths of the exogenous variables. This work attempts to visualize the problem and presents several simulated trajectories of a continuous time AR(2)‐process (Ornstein‐Uhlenbeck‐process) together with the observationally equivalent structures. Furthermore it is shown that aliasing can even change the analytical properties of the time paths of the system: whereas the first component of the Ornstein‐Uhlenbeck‐process is differentiable, the trajectories of the aliasing structures are continuous, but not differentiable any more.