Environmental variables that fluctuate randomly and dynamically over time, such as water
quality indices, are considered to be stochastic. They exhibit sub-exponential memory …

We present a standard form of master equations (MEs) for general one-dimensional non-
Markovian (history-dependent) jump processes, complemented by an asymptotic solution …

Moments play a crucial role for understanding the mathematical properties and practical
applications of Hawkes processes. Here, we derive expectations of Hawkes processes and …

Temporal Point Processes (TPPs) hold a pivotal role in modeling event sequences across
diverse domains, including social networking and e-commerce, and have significantly …

The Epidemic-Type Aftershock Sequences (ETAS) model and its variants effectively capture
the space-time clustering of seismicity, setting the standard for earthquake forecasting …

We study the continuous time limit of a self-exciting negative binomial process and discuss
the critical properties of its intensity distribution. In this limit, the process transforms into a …

抄録 価格ﾓﾃﾞﾙとして各ｲﾍﾞﾝﾄが他のｲﾍﾞﾝﾄを誘発させる自己励起性を持つ Hawkesprocess
は数多く用いられ, 因果関係を伴う経済現象の説明に用いられてきた. 特に価格変動の intensity に …

抄録 金融市場での価格変動の性質を理解するために確率過程を用いた価格モデルは数多く提案
されてきた. 特に各イベントが他のイベントの発生に影響を与える自己励起性を持つ Hawkes …