论文标题
自激发霍克斯过程的强度的非普遍力量法分布：一种现场理论方法
Non-universal power law distribution of intensities of the self-excited Hawkes process: a field-theoretical approach
论文作者
论文摘要
霍克斯自激发的点过程提供了许多物理，生物，地质和经济体系的爆发性间歇性动态。通过表达每单位时间下一个事件的概率（称为“强度”），例如地震，作为过去（可能）长期内存内核的所有事件的总和，霍克斯模型是非马克维亚的。通过将霍克斯模型映射到马尔可夫的随机部分微分方程上，我们就概率密度函数开发了一种现场理论方法。为了求解稳态方程，我们预测了接近关键点$ n = 1 $的概率密度函数（PDF）的功率定律扩展，其背景强度$ν_0$ n = 1 $，霍克斯强度的函数，霍克斯强度的函数，记忆kernel的平均时间尺度和分支$ n $ n $ n $ n $ n = 1 $。我们的理论预测通过数值模拟证实。
The Hawkes self-excited point process provides an efficient representation of the bursty intermittent dynamics of many physical, biological, geological and economic systems. By expressing the probability for the next event per unit time (called "intensity"), say of an earthquake, as a sum over all past events of (possibly) long-memory kernels, the Hawkes model is non-Markovian. By mapping the Hawkes model onto stochastic partial differential equations that are Markovian, we develop a field theoretical approach in terms of probability density functionals. Solving the steady-state equations, we predict a power law scaling of the probability density function (PDF) of the intensities close to the critical point $n=1$ of the Hawkes process, with a non-universal exponent, function of the background intensity $ν_0$ of the Hawkes intensity, the average time scale of the memory kernel and the branching ratio $n$. Our theoretical predictions are confirmed by numerical simulations.
