Exponential stability of impulsive jump linear systems with Markov process

The exponential stability is investigated for a class of continuous time linear systems with a finite state Markov chain form process and the impulsive jump at switching moments. The conditions, based on the average dwell time and the ratio of expectation of the total time running on all unstable subsystems to the expectation of the total time running on all stable subsystems,assure the exponential stability with a desired stability degree of the system irrespective of the impact of impulsive jump. The uniformly bounded result is realized for the case in which switched system is subjected to the impulsive effect of the excitation signal at some switching moments.

Exponential martingale for compound Poisson process with latent variable and its applications

In this article, we construct an exponential martingale for the compound Poisson process with latent variable. With the help of this exponential martingale, we provide an asymptotic behavior of the coherent entropic risk measure for the compound Poisson process and a deviation inequality for the ruin probability of the partly shifted risk process.

基于Ornstein-Uhlenbeck过程下具有两个再保险公司的比例再保险与投资

该文研究了两类风险模型下具有两个再保险公司的最优再保险和投资问题.保险公司购买比例再保险并投资于无风险资产和风险资产组成的金融市场,其风险资产价格模型受Ornstein-Uhlenbeck过程影响.假设再保险的保费按照指数保费原则来计算,保险公司的目标是使终端财富的期望指数效用最大化.利用随机控制理论和HJB方程,推导出了最优策略和值函数的显式表达式.最后,通过数值分析验证了模型参数对最优策略的影响.

MODERATE DEVIATIONS FOR PARAMETER ESTIMATORS IN FRACTIONAL ORNSTEIN-UHLENBECK PROCESS

We study moderate deviations for estimators of the drift parameter of the fractional Ornstein-Uhlenbeck process. Two moderate deviation principles are obtained.

PARAMETER ESTIMATION FOR AN ORNSTEIN-UHLENBECK PROCESS DRIVEN BY A GENERAL GAUSSIAN NOISE

In this paper,we consider an inference problem for an Ornstein-Uhlenbeck process driven by a general one-dimensional centered Gaussian process(G_(t))t≥0.The second order mixed partial derivative of the covariance function R(t,s)=E[GtGs]can be decomposed into two parts,one of which coincides with that of fractional Brownian motion and the other of which is bounded by(ts)^(β-1)up to a constant factor.This condition is valid for a class of continuous Gaussian processes that fails to be self-similar or to have stationary increments;some examples of this include the subfractional Brownian motion and the bi-fractional Brownian motion.Under this assumption,we study the parameter estimation for a drift parameter in the Ornstein-Uhlenbeck process driven by the Gaussian noise(G_(t))t≥0.For the least squares estimator and the second moment estimator constructed from the continuous observations,we prove the strong consistency and the asympotic normality,and obtain the Berry-Esséen bounds.The proof is based on the inner product's representation of the Hilbert space(h)associated with the Gaussian noise(G_(t))t≥0,and the estimation of the inner product based on the results of the Hilbert space associated with the fractional Brownian motion.

Parameter Estimation for Complex Ornstein-Uhlenbeck Processes

The drift parameter estimation problem of the complex Ornstein-Uhlenbeck process driven by a complexα-stable motion is considered.Based on discrete observations,an estimator of the unknown drift parameter is constructed by using the least squares method.Moreover,the strong consistency and the asymptotic distribution of the least squares estimator are derived under some assumptions.

ON COLLISION LOCAL TIME OF TWO INDEPENDENT FRACTIONAL ORNSTEIN-UHLENBECK PROCESSES

In this article, we study the existence of collision local time of two indepen- dent d-dimensional fractional Ornstein-Uhlenbeck processes X＋^H1 and Xt^H2 with different parameters Hi ∈ （0, 1）,i = 1, 2. Under the canonical framework of white noise analysis, we characterize the collision local time as a Hida distribution and obtain its＇ chaos expansion. Key words Collision local time; fractional Ornstein-Uhlenbeck processes; generalized white noise functionals; choas expansion

Stability of Stochastic Logistic Model with Ornstein-Uhlenbeck Process for Cell Growth of Microorganism in Fermentation Process

Current research is concerned with the stability of stochastic logistic equation with Ornstein-Uhlenbeck process. First, this research proves that the stochastic logistic model with Ornstein-Uhlenbeck process has a positive solution. After that, it also introduces the sufficient conditions for stochastically stability of stochastic logistic model for cell growth of microorganism in fermentation process for positive equilibrium point by using Lyapunov function. In addition, this research establishes the sufficient conditions for zero solution as mentioned in Appendix A due to the cell growth of microorganism μmax, which cannot be negative in fermentation process. Furthermore, for numerical simulation, current research uses the 4-stage stochastic Runge-Kutta (SRK4) method to show the reality of the results.

LEAST SQUARES TYPE ESTIMATION FOR DISCRETELY OBSERVED NON-ERGODIC GAUSSIAN ORNSTEIN-UHLENBECK PROCESSES

In this article, we consider the drift parameter estimation problem for the nonergodic Ornstein-Uhlenbeck process defined as dXt = OXtdt + dGt, i > 0 with an unknown parameter θ> 0, where G is a Gaussian process. We assume that the process {xt,t≥ 0} is observed at discrete time instants t1=△n,…, tn = n△n, and we construct two least squares type estimators θn and θn for θ on the basis of the discrete observations ,{xti,i= 1,…, n} as →∞. Then, we provide sufficient conditions, based on properties of G, which ensure that θn and θn are strongly consistent and the sequences √n△n(θn-θ) and √n△n(θn-θ) are tight. Our approach offers an elementary proof of [11], which studied the case when G is a fractional Brownian motion with Hurst parameter H∈(1/2, 1). As such, our results extend the recent findings by [11] to the case of general Hurst parameter H∈(0,1). We also apply our approach to study subfractional Ornstein-Uhlenbeck and bifractional Ornstein-Uhlenbeck processes.

THE LEAST SQUARES ESTIMATOR FOR AN ORNSTEIN-UHLENBECK PROCESS DRIVEN BY A HERMITE PROCESS WITH A PERIODIC MEAN

We consider the least square estimator for the parameters of Ornstein-Uhlenbeck processes dY_(s)=(∑_(j=1)^(k)μ_(j)φ_(j)(s)-βY_(s))ds+dZ_(s)^(q,H),driven by the Hermite process Z_(s)^(q,H)with order q≥1 and a Hurst index H∈(1/2,1),where the periodic functionsφ_(j)(s),,j=1,...,κare bounded,and the real numbersμ_(j),,j=1,...,κtogether withβ>0 are unknown parameters.We establish the consistency of a least squares estimation and obtain the asymptotic behavior for the estimator.We also introduce alternative estimators,which can be looked upon as an application of the least squares estimator.In terms of the fractional Ornstein-Uhlenbeck processes with periodic mean,our work can be regarded as its non-Gaussian extension.

ERRATUM TO： LEAST SQUARES ESTIMATION FOR ORNSTEIN-UHLENBECK PROCESSES DRIVEN BY THE WEIGHTED FRACTIONAL BROWNIAN MOTION （ACTA MATHEMATICA SCIENTIA 2016,36B （2） ：394-408）

We give a correction of Theorem 2.2 of Shen, Yin and Yan （2016）.

Exact Run Length Evaluation on a Two-Sided Modified ExponentiallyWeighted Moving Average Chart for Monitoring

A modified exponentially weighted moving average (EWMA) scheme is one of the quality control charts suchthat this control chart can quickly detect a small shift. The average run length (ARL) is frequently used for theperformance evaluation on control charts. This paper proposes the explicit formula for evaluating the average runlength on a two-sided modified exponentially weighted moving average chart under the observations of a first-orderautoregressive process, referred to as AR(1) process, with an exponential white noise. The performance comparisonof the explicit formula and the numerical integral technique is carried out using the absolute relative change forchecking the correct formula and the CPU time for testing speed of calculation. The results show that the ARL ofthe explicit formula and the numerical integral equation method are hardly different, but this explicit formula ismuch faster for calculating the ARL and offered accurate values. Furthermore, the cumulative sum, the classicalEWMA and the modified EWMA control charts are compared and the results show that the latter is better for smalland intermediate shift sizes. In addition, the explicit formula is successfully applied to real-world data in the healthfield as COVID-19 data in Thailand and Singapore.

SOME CHARACTERS OF A CLASS OF ORNSTEIN-UHLENBECK TYPE MARKOV PROCESSES WITH STABLE PROCESSES

This article concerns a class of Ornstein-Uhlenbeck type Markov processes and for which the level sets will be approached. By constructing a new class f processes, we shall obtain an inequality on the Hausdorff dimensions of the level sets for the Ornstein-Uhlenbeck type Markov processes. Based on this result, we finally verify that any two independent O-U.M.P with alpha-stable processes could collide with probability one.

DIMENSION RESULTS FORORNSTEIN-UHLENBECK TYPE MARKOVPROCESS

Let {X-t, t greater than or equal to 0} be an Ornstein-Uhlenbeck type Markov process with Levy process A(t), the authors consider the fractal properties of its ranges, give the upper and lower bounds of the Hausdorff dimensions of the ranges and the estimate of the dimensions of the level sets for the process. The existence of local times and occupation times of X-t are considered in some special situations.

QUASI-STATIONARY DISTRIBUTIONS FOR THE RADIAL ORNSTEIN-UHLENBECK PROCESSES

The purpose of this article is to obtain the quasi-stationary distributions of the δ（δ 〈 2）-dimensional radial Ornstein-Uhlenbeck process with parameter -λ by using the methods of Martinez and San Martin （2001）. It is described that the law of this process conditioned on first hitting 0 is just the probability measure induced by a （4 - δ）- dimensional radial Ornstein-Uhlenbeck process with parameter -λ. Moreover, it is shown that the law of the conditioned process associated with the left eigenfunction of the process conditioned on first hitting 0 is induced by a one-parameter diffusion.

Monoexponential Microsecond Decay of Blue Photoluminescence in Aged Porous Silicon Prepared with Ar^(+) 488nm

Blue photoluminescence is observed in aged porous silicon samples anodized under Ar^(+)488 nm laser illumination.No samples have been undergone any heating treatment process.Both nanosecond and microsecond decay of blue photoluminescence have been measured.Samples show a good monoexponential microsecond decay with lifetimes of about 5.3μs.Photoluminescence excitation spectra of blue and red Photoluminescence indicate there is a large Stokes shift(about 800-900meV)in the excitation spectra of red photoluminescence while no this marked Stokes shift in that of blue photoluminescence.The possible origin of the photoluminescence is discussed based on the experimental results.

Hyper-exponential jump-diffusion model under the barrier dividend strategy

In this paper, we consider a hyper-exponential jump-diffusion model with a constant dividend barrier. Explicit solutions for the Laplace transform of the ruin time, and the Gerber- Shiu function are obtained via martingale stopping.

Asymptotic Properties of Estimators for Ornstein-Uhlenbeck Processes with Small Symmetricα-Stable Motions

The asymptotic behaviors for estimators of the drift parameters in the Ornstein-Uhlenbeck process driven by small symmetricα-stable motion are studied in this paper.Based on the discrete observations,the conditional least squares estimators(CLSEs)of all the parameters involved in the Ornstein–Uhlenbeck process are proposed.We establish the consistency and the asymptotic distributions of our estimators asεgoes to 0 and n goes to∞simultaneously.

利用SE-GPR模型对甲醇/柴油混合燃料柴油机性能的预测

为了对柴油机的经济性和排放参数进行高效、准确的预测,根据4190型船用柴油机实验数据与边界参数,建立AVL-BOOST甲醇/柴油混合燃料柴油机仿真模型;利用模型进行仿真实验,并建立甲醇掺混比、废气再循环(exhaust gas recirculation,EGR)率、喷油提前角和进气压力4个控制参数对有效油耗率和NO x排放预测数据集;利用该数据集对5种不同核函数的高斯过程回归(Gaussian process regression,GPR)模型进行训练;最后将最优的平方指数高斯过程回归(squared exponential-Gaussian process regression,SE-GPR)模型、AVL-BOOST仿真数据和柴油机实验数据进行对比。结果表明:在数据量为180组时,SE-GPR模型对有效油耗率和NO x排放均取得拟合关联度99%以上,均方根误差(root mean square error,RMSE)分别为1.859,0.3445,平均绝对误差(mean absolute error,MAE)分别为0.954,0.2489;并且,相较于AVL-BOOST仿真实验,SE-GPR模型对实验数据具有更好的拟合性。

智能电网用电异常诊断和调控策略

为了针对智能电网不同异常用电的原因制定分类调整方法,提出了基于二次根式函数电价调整和计算定界的策略,该策略基于自动过程控制和模糊综合评价进行监控、诊断及分类调整。首先,通过指数加权移动平均值作为自动过程控制的控制变量并确定上下界来监控用电量,建立监控模型;其次,用模糊综合评价法诊断异常用电原因;最后,根据不同原因制定分类调整策略,建立电价需求响应调整模型。算例仿真结果表明,提出的基于二次根式函数电价调整策略在调整频次、残差标准误差、全社会福利和电力公司利润等方面均优于线性函数调整。应用模糊综合评价方法能有效分析异常用电原因,制定分类调整策略能消除异常并获得平稳波动用电量。