The Hawkes self-excited point process provides an efficient representation of the bursty
intermittent dynamics of many physical, biological, geological, and economic systems. By …

The origin (s) of the ubiquity of probability distribution functions with power law tails is still a
matter of fascination and investigation in many scientific fields from linguistic, social …

The linear Hawkes point process is a first-order non-Markovian stochastic model of
intermittent bursty dynamics. While its nonlinear extensions, called nonlinear Hawkes …

Eulerian-Lagrangian models of particle-laden (multiphase) flows describe fluid flow and
particle dynamics in the Eulerian and Lagrangian frameworks respectively. Regardless of …

Hawkes processes are a type of point process that models self-excitement among time
events. They have been used in a myriad of applications, ranging from finance and …

The arguably most important paradox of financial economics—the excess volatility puzzle—
first identified by Robert Shiller in 1981 states that asset prices fluctuate much more than …

Transitions between metastable equilibria in the low-temperature phase of dynamical Ising
game with activity spillover are studied in the infinite time limit. It is shown that exponential …

Eulerian-Lagrangian models describe fluid flow and particle dynamics in the Eulerian and
Lagrangian frameworks, respectively. In chaotic systems the particle dynamics are …

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

The Hawkes process is a self-exciting Poisson point process, characterised by a conditional
intensity function. Since its introduction fifty years ago, it has been the subject of numerous …