A Double Shot Noise Process and Its Application in Insurance

The authors consider a compound Cox model of insurance risk with the additional economic assumption of a positive interest rate. As the authors note a duality result relating a compound Cox model of insurance risk with a positive interest rate and a double shot noise process, the authors analyze a double shot noise process systematically for its theoretical distributional properties, based on the piecewise deterministic Markov process theory, and the martingale methodology. The authors also obtain the moments of aggregate accumulated/discounted claims where the claim arrival process follows a Cox process with shot noise intensity. Removing the parameters in a double shot noise process gradually, the authors show that it becomes a compound Cox process with shot noise intensity, a single shot noise process and a compound Poisson process. Numerical comparisons are shown between the moments （i.e. means and variances） of a compound Poisson model and their counterparts of a compound Cox model with/without considering a positive interest rate. For that purpose, the authors assume that claim sizes and primary event sizes follow an exponential distribution, respectively.

Description of time-varying noise processes with applications to aircraft flying-over noise

On the basis of spectrum moment description of a signal, evolutionary vector is developed to describe slowly time-varying noise processes. It describes the main time-varying properties of a signal. Applications to aircraft flying-over noise are presented.

Process Noise Parameters of Beamforming Green Nodes

Signals arrive out of phase at the intended receiver from collaborative beamforming （CB） nodes due to the instability in the output frequency signals of the universal software radio peripheral＇s （USRP） local oscillator （LO）. These nodes including the target must synchronize their oscillator frequencies for coherent signal reception. In order to do this, frequencies and phases of the signals should be estimated in software defined radio （SDR） and smoothen with nonlinear filters such as the extended Kalman filter （EKF）. The process noise parameters of the NI USRP-2920 nodes will have to be calculated and used with the EKF process noise covariance matrix. These nodes are green communication hardware devices where most of the hardware units are now software defined. This article uses the direct spectrum method to obtain the phase noise values at various frequency offsets of the NI USRP-2920 in order to calculate the power spectral density of fractional frequency fluctuation. By applying the power-law noise model to this obtained value, the generated white frequency noise and random walk frequency noise values are q_1=1.93x10^-21 and q_2=5.86x10^-18, respectively.

Selection of noise parameters for Kalman filter

The Bayesian probabilistic approach is proposed to estimate the process noise and measurement noise parameters for a Kalman filter. With state vectors and covariance matrices estimated by the Kalman filter, the likehood of the measurements can be constructed as a function of the process noise and measurement noise parameters. By maximizing the likelihood function with respect to these noise parameters, the optimal values can be obtained. Furthermore, the Bayesian probabilistic approach allows the associated uncertainty to be quantified. Examples using a single-degree-of-freedom system and a ten-story building illustrate the proposed method. The effect on the performance of the Kalman filter due to the selection of the process noise and measurement noise parameters was demonstrated. The optimal values of the noise parameters were found to be close to the actual values in the sense that the actual parameters were in the region with significant probability density. Through these examples, the Bayesian approach was shown to have the capability to provide accurate estimates of the noise parameters of the Kalman filter, and hence for state estimation.

Interference Mitigation Techniques Using Receiver Processing and Resource Allocation

Heterogeneous network consists of the pico cells overlaid over the macro cell coverage area in a wireless cellular network. The pico cells are deployed to increase the capacity of the homogeneous network by reusing the spectrum further. However, more users will tend to be associated to the macro cell due to the fact that the transmit power of the pico cell is low. In order to increase the number of users associated to the pico cell, range extension techniques like biased association are used. This will cause severe interference to cell edge users of the pico cell from the macro cell causing degradation in throughput performance in the cell range extension area. In this paper, interference mitigation using receiver processing along with different scheduling techniques is proposed to improve the throughput, average delay, and the packet delivery ratio performance of the system. The performance comparison of the round robin, proportional fair and modified largest weighted delay first (MLWDF) algorithm for resource allocation using interference suppressing receiver is done, and analyzed. It is shown that the MLWDF algorithm achieves the highest throughput with minimum average delay of packets with the best delivery ratio.

The maximal Lyapunov exponent of a co-dimension two-bifurcation system excited by a bounded noise

In the present paper, the maximal Lyapunov ex- ponent is investigated for a co-dimension two bifurcation system that is on a three-dimensional central manifold and subjected to parametric excitation by a bounded noise. By using a perturbation method, the expressions of the invari- ant measure of a one-dimensional phase diffusion process are obtained for three cases, in which different forms of the matrix B, that is included in the noise excitation term, are assumed and then, as a result, all the three kinds of singular boundaries for one-dimensional phase diffusion process are analyzed. Via Monte-Carlo simulation, we find that the an- alytical expressions of the invariant measures meet well the numerical ones. And furthermore, the P-bifurcation behav- iors are investigated for the one-dimensional phase diffusion process. Finally, for the three cases of singular botmdaries for one-dimensional phase diffusion process, analytical ex- pressions of the maximal Lyapunov exponent are presented for the stochastic bifurcation system.

Time Series Analysis on Reported Cases of Tuberculosis in Minna Niger State Nigeria

Predicting the trend of non-seasonal data is a difficult task in Social Science. In this research work, we used time series analysis of 144 observations on monthly basis for record of reported cases of tuberculosis patients in Minna General Hospital, Niger State from the period of 2007-2018. Exploratory Data Analysis (EDA: Time Plot and Descriptive Statistics), Stationarity Test (ADF), Trend estimation (Tt), Normality Test, and Forecast evaluation were carried out. The Augmented Dickey Fuller test for stationarity was conducted and the result revealed that the series are not stationary but became stationary after first difference. The correlogram established that the ARIMA (2, 1, 3) was the best model this was further confirmed from the result of L-jung Box. Equation for ARIMA (2, 1, 3) was given as Xt + 0.6867Xt-1 – 0.8859Xt-2 = Et + 1.3077Et-1 - 1.2328Et-2 + 0.5788Et-3. Which was used to predict five years likely cases of tuberculosis in Minna for the period of 2019-2023. It was clearly shown from the projection that the reported cases of tuberculosis reduce year by year by 7% over the period under consideration which could be as a result of intervention from government, health worker, and individuals. In line with these findings, we recommend that the management of general hospital to increase awareness campaign to the public on the causes and dangers of tuberculosis.

On the Effects of Different Interpretations of Stochastic Differential Equations

This paper addresses the problem of the interpretation of the stochastic differential equations (SDE). Even if from a theoretical point of view, there are infinite ways of interpreting them, in practice only Stratonovich’s and Itô’s interpretations and the kinetic form are important. Restricting the attention to the first two, they give rise to two different Fokker-Planck-Kolmogorov equations for the transition probability density function (PDF) of the solution. According to Stratonovich’s interpretation, there is one more term in the drift, which is not present in the physical equation, the so-called spurious drift. This term is not present in Itô’s interpretation so that the transition PDF’s of the two interpretations are different. Several examples are shown in which the two solutions are strongly different. Thus, caution is needed when a physical phenomenon is modelled by a SDE. However, the meaning of the spurious drift remains unclear.

Flexible polarization demultiplexing method based on an adaptive process noise covariance Kalman filter

A flexible polarization demultiplexing method based on an adaptive Kalman filter（AKF） is proposed in which the process noise covariance has been estimated adaptively. The proposed method may significantly improve the adaptive capability of an extended Kalman filter（EKF） by adaptively estimating the unknown process noise covariance. Compared to the conventional EKF, the proposed method can avoid the tedious and time consuming parameter-by-parameter tuning operations. The effectiveness of this method is confirmed experimentally in 128 Gb/s 16 QAM polarization-division-multiplexing（PDM） coherent optical transmission systems. The results illustrate that our proposed AKF has a better tracking accuracy and a faster convergence（about 4 times quicker）compared to a conventional algorithm with optimal process noise covariance.

Effect of cutting process on machine tool noise

Based on the principle of Statistical Energy Analysis (SEA) for non-conservatively coupled systems under general excitations, relationship between noise radiated from and excitations on coupled complex structures is studied, which lays a foundation for the determination of noise/vibration energy by evaluation of exciting forces, and from that the quantitative analysis of the effects of an excitation on sound power from a sub-structure can be done. With extending of the relationship to the study of cutting noise, regression analysis method for evaluating the effects of cutting process on machine tool noise is established. Results show that cutting process has generally negligible effects on machine tool noise, and there is no apparent difference between machine tool noise in cutting condition and in idle one.

STATISTIC PROPERTIES OF NOISE FIELD OF MOVING SOURCE IN SHALLOW WATER AND ITS EFFECTS ON SIGNAL PROCESSING FOR THE NOISE RANGING SONAR

In this paper the properties of space- time correlation function of the noise field of moving source in layered statistic inhomogeneous medium are studied and the effects of random fluctuating boundary are considered as well.It has been shown, theoretically and experimentally, multi-path propergating effects cause the dispersion of the correlation function and fluctuations of the medium refraction index and the boundary cause the fluctuation of it.The effect of the movement of the noise source on the output of real- time correlator is equivalent to a low- pass filter added the drift of space- time correlation function.These properties of the correlation function cause grave degradation of the signal processing gain of noise ranging sonar system.The fluctuating and the distortion of conrrelation function made it difficult to realize the noise ranging.So in this paper, a method of space correlation ranging by a linear array of four points with short separation and long span and a technigue of dual- correlation signal processing are presented. By this, the influences of previously mentioned factors are greatly overcomed.Futhermore, for the long period and great delay fluctuation of the dual- correlation function output caused by internal wave, a method of limited memory Quasi- Kalman filtering is developed and the effective accurate ranging and tracing of noise ranging sonar are able to be tralized finally.

Data-driven discovery of linear dynamical systems from noisy data

In modern science and engineering disciplines,data-driven discovery methods play a fundamental role in system modeling,as data serve as the external representations of the intrinsic mechanisms within systems.However,empirical data contaminated by process and measurement noise remain a significant obstacle for this type of modeling.In this study,we have developed a data-driven method capable of directly uncovering linear dynamical systems from noisy data.This method combines the Kalman smoothing and sparse Bayesian learning to decouple process and measurement noise under the expectation-maximization framework,presenting an analytical method for alternate state estimation and system identification.Furthermore,the discovered model explicitly characterizes the probability distribution of process and measurement noise,as they are essential for filtering,smoothing,and stochastic control.We have successfully applied the proposed algorithm to several simulation systems.Experimental results demonstrate its potential to enable linear dynamical system discovery in practical applications where noise-free data are intractable to capture.

Valuation of CDS counterparty risk under a reduced-form model with regime-switching shot noise default intensities

We study the counterparty risk for a credit default swap （CDS） in a regime-switching market driven by an underlying continuous-time Markov chain. We model the default dependence via some correlated Cox processes with regime-switching shot noise intensities containing common shock. Under the proposed model, the general bilateral counterparty risk pricing formula for CDS contracts with the possibility of joint defaults is presented. Based on some expressions for the conditional Laplace transform of the integrated intensity processes, semi-analytical solution for the bilateral credit valuation adjustment （CVA） is derived. When the model parameters satisfy some conditions, explicit formula for the bilateral CVA at time 0 is also given.

Dynamic State Estimation of Medium-voltage DC Integrated Power System with Pulse Load

The dynamic characteristic evaluation is an important prerequisite for safe and reliable operation of the mediumvoltage DC integrated power system(MIPS),and the dynamic state estimation is an essential technical approach to the evaluation.Unlike the electromechanical transient process in a traditional power system,periodic change in pulse load of the MIPS is an electromagnetic transient process.As the system state suddenly changes in the range of a smaller time constant,it is difficult to estimate the dynamic state due to periodic disturbance.This paper presents a dynamic mathematical model of the MIPS according to the network structure and control strategy,thereby overcoming the restrictions of algebraic variables on the estimation and developing a dynamic state estimation method based on the extended Kalman filter.Using the method of adding fictitious process noise,it is possible to solve the problem that the linearized algorithm of the MIPS model is less reliable when an abrupt change occurs in the pulse load.Therefore,the accuracy of the dynamic state estimation and the stability of the filter can be improved under the periodic disturbance of pulse load.The simulation and experimental results confirm that the proposed model and method are feasible and effective.