We propose an extension to Hawkes processes by treating the levels of
self-excitation as a stochastic differential equation. Our new point process
allows better approximation in application domains where events and intensities
accelerate each other with correlated levels of contagion. We generalize a
recent algorithm for simulating draws from Hawkes processes whose levels of
excitation are stochastic processes, and propose a hybrid Markov chain Monte
Carlo approach for model fitting. Our sampling procedure scales linearly with
the number of required events and does not require stationarity of the point
process. A modular inference procedure consisting of a combination between
Gibbs and Metropolis Hastings steps is put forward. We recover expectation
maximization as a special case. Our general approach is illustrated for
contagion following geometric Brownian motion and exponential Langevin
dynamics.

通过将自激励水平视为随机微分方程，我们提出了对 Hawkes 过程的扩展，该新点过程允许更好地逼近事件和强度相互加速且传染性相关水平的应用领域。我们推广了一种最近用于模拟具有随机激发水平的 Hawkes 过程的算法，并提出了混合马尔可夫链蒙特卡罗方法来拟合模型。我们的采样过程与所需事件的数量呈线性比例，并且不需要点过程的平稳性。我们提出了一种由 Gibbs 和 Metropolis Hastings 步骤组合而成的模块化推断过程。我们将期望最大化作为特例。这种一般方法是通过几何布朗运动和指数朗之万动力学的传染研究进行了说明。