本文研究了一类高非线性的带Poisson跳的随机时变时滞微分方程。运用Lyapunov函数方法、随机分析和代数不等式技巧,研究了该类方程全局解的存在性。This paper investigates a class of stochastic time-varying delay differential equ...本文研究了一类高非线性的带Poisson跳的随机时变时滞微分方程。运用Lyapunov函数方法、随机分析和代数不等式技巧,研究了该类方程全局解的存在性。This paper investigates a class of stochastic time-varying delay differential equations(STVDEs) with Poisson jump. By employing the Lyapunov functions method, stochas-tic analysis and algebraic inequality techniques, the existence of the global solution toa STVDE with Poisson jump is obtained.展开更多
在数字经济时代,随着电子商务快速发展,银行软件系统的规模显著扩大,软件故障跟踪系统中故障的报告存在随机性、不规律性以及各种不确定因素,因此故障检测过程可以看作是一个随机过程。在软件可靠性领域,随机微分方程常用于描述软件故...在数字经济时代,随着电子商务快速发展,银行软件系统的规模显著扩大,软件故障跟踪系统中故障的报告存在随机性、不规律性以及各种不确定因素,因此故障检测过程可以看作是一个随机过程。在软件可靠性领域,随机微分方程常用于描述软件故障的发生过程及其可靠性的动态变化,在故障检测率方面,广义拐点S型故障检测率往往具有更强的灵活性,因此本文提出一种基于随机微分方程和广义拐点S型故障检测率的软件可靠性模型,并使用极大似然估计方法对模型的参数进行估计。最后在A银行测试中心数据集上进行验证,实验结果表明本文提出模型对实验数据拟合效果最好。因此该模型相较于其他经典软件可靠性模型具有优越性。In the era of digital economy, with the rapid development of e-commerce, the scale of banking software systems has expanded significantly, and the fault reporting in the software fault tracking system has randomness, irregularity and various uncertain factors, so the fault detection process can be regarded as a random process. In the field of software reliability, stochastic differential equations are often used to describe the occurrence process of software failures and the dynamic changes of their reliability, and the generalized inflection point S-type fault detection rate is often more flexible in terms of fault detection rate, so this paper proposes a software reliability model based on stochastic differential equations and generalized inflection point S-type fault detection rate, and uses the maximum likelihood estimation method to estimate the parameters of the model. Finally, it is verified on the data set of A Bank test center, and the experimental results show that the proposed model has the best fitting effect on the experimental data. Therefore, this model has advantages over other classical software reliability models.展开更多
文摘本文研究了一类高非线性的带Poisson跳的随机时变时滞微分方程。运用Lyapunov函数方法、随机分析和代数不等式技巧,研究了该类方程全局解的存在性。This paper investigates a class of stochastic time-varying delay differential equations(STVDEs) with Poisson jump. By employing the Lyapunov functions method, stochas-tic analysis and algebraic inequality techniques, the existence of the global solution toa STVDE with Poisson jump is obtained.
文摘在数字经济时代,随着电子商务快速发展,银行软件系统的规模显著扩大,软件故障跟踪系统中故障的报告存在随机性、不规律性以及各种不确定因素,因此故障检测过程可以看作是一个随机过程。在软件可靠性领域,随机微分方程常用于描述软件故障的发生过程及其可靠性的动态变化,在故障检测率方面,广义拐点S型故障检测率往往具有更强的灵活性,因此本文提出一种基于随机微分方程和广义拐点S型故障检测率的软件可靠性模型,并使用极大似然估计方法对模型的参数进行估计。最后在A银行测试中心数据集上进行验证,实验结果表明本文提出模型对实验数据拟合效果最好。因此该模型相较于其他经典软件可靠性模型具有优越性。In the era of digital economy, with the rapid development of e-commerce, the scale of banking software systems has expanded significantly, and the fault reporting in the software fault tracking system has randomness, irregularity and various uncertain factors, so the fault detection process can be regarded as a random process. In the field of software reliability, stochastic differential equations are often used to describe the occurrence process of software failures and the dynamic changes of their reliability, and the generalized inflection point S-type fault detection rate is often more flexible in terms of fault detection rate, so this paper proposes a software reliability model based on stochastic differential equations and generalized inflection point S-type fault detection rate, and uses the maximum likelihood estimation method to estimate the parameters of the model. Finally, it is verified on the data set of A Bank test center, and the experimental results show that the proposed model has the best fitting effect on the experimental data. Therefore, this model has advantages over other classical software reliability models.
