This paper mainly investigates the effect of the lévy jumps on the stochastic HIV infection model with cytotoxic T lymphocytes (CTLs) immune response. First, we prove that there is a unique global positive soluti...This paper mainly investigates the effect of the lévy jumps on the stochastic HIV infection model with cytotoxic T lymphocytes (CTLs) immune response. First, we prove that there is a unique global positive solution in any population dynamics, then we find sufficient conditions for the extinction of the disease. For proofing the persistence in mean, a special Lyapunov function be established, we obtain that if the infected CD4<sup>+</sup> T-cells and virus particles will persistence in mean. Finally, numerical simulations are carried out to illustrate the theoretical results.展开更多
研究了一类具有时滞与Lévy跳的随机捕食者-食饵模型.首先利用Lyapunov方法和It o ^公式,给出了模型全局正解的存在唯一性.然后根据切比雪夫不等式和指数鞅不等式以及Borel-Cantelli引理等,得到了解的随机最终有界性以及灭绝性.最后...研究了一类具有时滞与Lévy跳的随机捕食者-食饵模型.首先利用Lyapunov方法和It o ^公式,给出了模型全局正解的存在唯一性.然后根据切比雪夫不等式和指数鞅不等式以及Borel-Cantelli引理等,得到了解的随机最终有界性以及灭绝性.最后,运用数值模拟验证了理论结果.展开更多
With the development of information technology,rumors propagate faster and more widely than in the past.In this paper,a stochastic rumor propagation model incorporating media coverage and driven by Lévy noise is ...With the development of information technology,rumors propagate faster and more widely than in the past.In this paper,a stochastic rumor propagation model incorporating media coverage and driven by Lévy noise is proposed.The global positivity of the solution process is proved,and further the basic reproductive number R_(0) is obtained.When R_(0)<1,the dynamical process of system with Lévy jump tends to the rumor-free equilibrium point of the deterministic system,and the rumor tends to extinction;when R_(0)>1,the rumor will keep spreading and the system will oscillate randomly near the rumor equilibrium point of the deterministic system.The results show that the oscillation amplitude is related to the disturbance of the system.In addition,increasing media coverage can effectively reduce the final spread of rumors.Finally,the above results are verified by numerical simulation.展开更多
文摘This paper mainly investigates the effect of the lévy jumps on the stochastic HIV infection model with cytotoxic T lymphocytes (CTLs) immune response. First, we prove that there is a unique global positive solution in any population dynamics, then we find sufficient conditions for the extinction of the disease. For proofing the persistence in mean, a special Lyapunov function be established, we obtain that if the infected CD4<sup>+</sup> T-cells and virus particles will persistence in mean. Finally, numerical simulations are carried out to illustrate the theoretical results.
基金Program for Professor of Special Appointment(Eastern Scholar)at Shanghai Institutions of Higher Learning,and the Project for the Natural Science Foundation of Shanghai(Grant No.21ZR1444100)the Project for the National Natural Science Foundation of China(Grant Nos.71774111,61702331,71871144).
文摘With the development of information technology,rumors propagate faster and more widely than in the past.In this paper,a stochastic rumor propagation model incorporating media coverage and driven by Lévy noise is proposed.The global positivity of the solution process is proved,and further the basic reproductive number R_(0) is obtained.When R_(0)<1,the dynamical process of system with Lévy jump tends to the rumor-free equilibrium point of the deterministic system,and the rumor tends to extinction;when R_(0)>1,the rumor will keep spreading and the system will oscillate randomly near the rumor equilibrium point of the deterministic system.The results show that the oscillation amplitude is related to the disturbance of the system.In addition,increasing media coverage can effectively reduce the final spread of rumors.Finally,the above results are verified by numerical simulation.
文摘考虑金融时间序列发生的跳跃、随机波动率和"杠杆效应",建立由不同Lévy过程驱动的非高斯OU随机波动模型.通过结构保持等价鞅测度变换和FFT技术,对不同Lévy过程驱动下的非高斯OU(non-Gaussian Ornstein-Uhlenbeck process)期权定价问题进行研究.同时,在结构保持等价鞅测度下,推导出不同Lévy过程驱动下BNS模型离散化表达形式,并构建了基于SMC(sequential Monte Carlo)的极大似然估计、联合样本估计、梯度-SMC估计的非高斯OU期权定价模型参数估计方法.实证研究中,采用近470万个S&P500期权价格数据,从样本内拟合效果、样本外预测、模型稳定性、综合矫正风险几个方面,对不同Lévy过程驱动的非高斯OU期权定价模型、参数估计方法以及期权定价效果进行全面系统研究.实证研究表明,所有模型对实值期权的定价效果要优于虚值期权.本文基于联合样本估计和梯度-SMC估计的非高斯OU期权定价模型具有明显的优势.
