Related papers: Burst and inter-burst duration statistics as empir…
We introduce a generalisation of the well-known ARCH process, widely used for generating uncorrelated stochastic time series with long-term non-Gaussian distributions and long-lasting correlations in the (instantaneous) standard deviation…
We consider Stochastic Volatility processes with heavy tails and possible long memory in volatility. We study the limiting conditional distribution of future events given that some present or past event was extreme (i.e. above a level which…
We consider a generic class of stochastic particle-based models whose state at an instant in time is described by a set of continuous degrees of freedom (e.g. positions), and the length of this set changes stochastically in time due to…
We introduce a stochastic nonlocal reaction--diffusion model arising in tumour dynamics. Spatial dispersal is described by the fractional Laplacian, accounting for anomalous diffusion and long--range relocation events. The system is…
We study the activity, i.e., the number of transactions per unit time, of financial markets. Using the diffusion entropy technique we show that the autocorrelation of the activity is caused by the presence of peaks whose time distances are…
Recurrent boom-and-bust cycles are a salient feature of economic and financial history. Cycles found in the data are stochastic, often highly persistent, and span substantial fractions of the sample size. We refer to such cycles as "long".…
Fast radio bursts (FRBs) are millisecond-duration radio signals occurring at cosmological distances. However the physical model of FRBs is mystery, many models have been proposed. Here we study the frequency distributions of peak flux,…
Long-term temporal correlations in time series in a form of an event sequence have been characterized using an autocorrelation function (ACF) that often shows a power-law decaying behavior. Such scaling behavior has been mainly accounted…
We analyze the hitting time distributions of stock price returns in different time windows, characterized by different levels of noise present in the market. The study has been performed on two sets of data from US markets. The first one is…
We consider stochastic point processes generating time series exhibiting power laws of spectrum and distribution density (Phys. Rev. E 71, 051105 (2005)) and apply them for modeling the trading activity in the financial markets and for the…
We study exclusion processes on the integer lattice in which particles change their velocities due to stickiness. Specifically, whenever two or more particles occupy adjacent sites, they stick together for an extended period of time, and…
We study the long memory of order flow for each of three liquid currency pairs on a large electronic trading platform in the foreign exchange (FX) spot market. Due to the extremely high levels of market activity on the platform, and in…
Stochastic systems with memory naturally appear in life science, economy, and finance. We take the modelling point of view of stochastic functional delay equations and we study these structures when the driving noises admit jumps. Our…
We consider the problem of leakage or effusion of an ensemble of independent stochastic processes from a region where they are initially randomly distributed. The case of Brownian motion, initially confined to the left half line with…
Many recent studies use individual longitudinal data to analyze job search behaviors. Such data allow the use of fixed-effects models, which supposedly address the issue of dynamic selection and make it possible to identify the structural…
In this work we introduce a variant of the Yule-Simon model for preferential growth by incorporating a finite kernel to model the effects of bounded memory. We characterize the properties of the model combining analytical arguments with…
Temporal inhomogeneities observed in various natural and social phenomena have often been characterized in terms of scaling behaviors in the autocorrelation function with a decaying exponent $\gamma$, the interevent time distribution with a…
Long and short memory in economic processes is usually described by the so-called discrete fractional differencing and fractional integration. We prove that the discrete fractional differencing and integration are the Grunwald-Letnikov…
We propose a generalization of the widely used fractional Brownian motion (FBM), memory-multi-FBM (MMFBM), to describe viscoelastic or persistent anomalous diffusion with time-dependent memory exponent $\alpha(t)$ in a changing environment.…
We study the motion of a one-dimensional particle which reverses its direction of acceleration stochastically. We focus on two contrasting scenarios, where the waiting-times between two consecutive acceleration reversals are drawn from (i)…