Generalized local and nonlocal master equations for some stochastic processes

Zhao, Yanxiang; Wang, Jiakou; Ma, Yingjin; Du, Qiang

doi:10.1016/j.camwa.2015.09.030

Cited by 5 publications

(3 citation statements)

References 27 publications

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“…Kinetic derivation method [91] would effectively work in such a situation. We then must use a conservative implicit scheme to handle the nonlocal terms efficiently.…”

Section: Discussionmentioning

confidence: 99%

HJB and Fokker-Planck equations for river environmental management based on stochastic impulse control with discrete and random observation

Yoshioka

Tsujimura

Hamagami

et al. 2021

Computers & Mathematics with Applications

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“…Kinetic derivation method [91] would effectively work in such a situation. We then must use a conservative implicit scheme to handle the nonlocal terms efficiently.…”

Section: Discussionmentioning

confidence: 99%

HJB and Fokker-Planck equations for river environmental management based on stochastic impulse control with discrete and random observation

Yoshioka

Tsujimura

Hamagami

et al. 2021

Computers & Mathematics with Applications

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“…where γ(x , x, t) denotes the transition rate from x to x at time t. Assume that the Markov process is time-homogeneous, namely γ(x , x, t) = γ(x , x). Then in the discrete time form [29], Eq. ( 20) is often reformulated as…”

Section: Markov Jump Processmentioning

confidence: 99%

Nonlocal Neural Networks, Nonlocal Diffusion and Nonlocal Modeling

Tao,

Sun,

et al. 2018

Preprint

Self Cite

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Nonlocal neural networks [25] have been proposed and shown to be effective in several computer vision tasks, where the nonlocal operations can directly capture long-range dependencies in the feature space. In this paper, we study the nature of diffusion and damping effect of nonlocal networks by doing spectrum analysis on the weight matrices of the well-trained networks, and then propose a new formulation of the nonlocal block. The new block not only learns the nonlocal interactions but also has stable dynamics, thus allowing deeper nonlocal structures. Moreover, we interpret our formulation from the general nonlocal modeling perspective, where we make connections between the proposed nonlocal network and other nonlocal models, such as nonlocal diffusion process and Markov jump process.

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“…Thus, it is of much interest to consider nonlocal model to understand and control complex processes. Under this circumstance, many researchers established the nonlocal model, such as non-Markovian jump processes, Levy flights [ 9 – 11 ], fractional differential operators [ 12 – 14 ] and so on.…”

Section: Introductionmentioning

confidence: 99%

Stability analysis of a nonlocal SIHRDP epidemic model with memory effects

Chen

et al. 2022

Nonlinear Dyn

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The prediction and control of COVID-19 is critical for ending this pandemic. In this paper, a nonlocal SIHRDP (S-susceptible class, I-infective class (infected but not hospitalized), H-hospitalized class, R-recovered class, D-death class and P-isolated class) epidemic model with long memory is proposed to describe the multi-wave peaks for the spread of COVID-19. Based on the basic reproduction number , which is completely controlled by fractional order, the stability of the proposed system is studied. Furthermore, the numerical simulation is conducted to gauge the performance of the proposed model. The results on Hunan, China, reveal that suggests that the disease-free equilibrium point is globally asymptotically stable. Likewise, the situation of the multi-peak case in China is presented, and it is clear that the nonlocal epidemic system has a superior fitting effect than the classical model. Finally an adaptive impulsive vaccination is introduced based on the proposed system. Then employing the real data of France, India, the USA and Argentina, parameters identification and short-term forecasts are carried out to verify the effectiveness of the proposed model in describing the case of multiple peaks. Moreover, the implementation of vaccine control is expected once the hospitalized population exceeds of the total population. Numerical results of France, Indian, the USA and Argentina shed light on the varied effect of vaccine control in different countries. According to the vaccine control imposed on France, no obvious effect is observed even consider reducing human contact. As for India, although there will be a temporary increase in hospitalized admissions after execution of vaccination control, COVID-19 will eventually disappear. Results on the USA have seen most significant effect of vaccine control, the number of hospitalized individuals drops off and the disease is eventually eradicated. In contrast to the USA, vaccine control in Argentina has also been very effective, but COVID-19 cannot be completely eradicated.

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Generalized local and nonlocal master equations for some stochastic processes

Cited by 5 publications

References 27 publications

HJB and Fokker-Planck equations for river environmental management based on stochastic impulse control with discrete and random observation

HJB and Fokker-Planck equations for river environmental management based on stochastic impulse control with discrete and random observation

Nonlocal Neural Networks, Nonlocal Diffusion and Nonlocal Modeling

Stability analysis of a nonlocal SIHRDP epidemic model with memory effects

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