论文标题
与长度内存可变的霍克斯工艺相互作用的完美模拟
Perfect simulation for interacting Hawkes processes with variable length memory
论文作者
论文摘要
我们考虑具有可变长度存储器的非线性多元霍克斯过程，该过程允许通过其膜电位来描述神经元网络的活性。我们提出了该过程的图形结构，并通过完美的模拟算法构建了该过程的固定版本。通过提出一个假设，即在i $中的神经元$ i \的峰值率$β_i$是有限的，我们基于Poisson Process $（m^i，i \ in I）$的先验实现构建算法。我们表明，存在一个临界值$Δ_C$，以便如果$ \ usewexu>δ_c$（其中$ \useSuessΔ= \ inf_i {δ_i} $带有$δ_i= \ frac {β_{β_{β_{i*}}}
We consider a nonlinear multivariate Hawkes process having a variable length memory which allows to describe the activity of a neuronal network by its membrane potential. We propose a graphical construction of the process and we construct, by means of a perfect simulation algorithm, a stationary version of the process. By making the hypothesis that the spiking rate $β_i$ of the neuron $i \in I $ is bounded, we construct an algorithm based on a priori realizations of the Poisson process $(M^i, i \in I)$. We show that there exists a critical value $δ_c$ such that if $\underlineδ > δ_c$ (where $\underlineδ= \inf_i{δ_i}$ with $δ_i = \frac{β_{i* }}{β^*_i-β_{i*}}$ ) the process is ergodic.
