Related papers: Fractional stochastic model of citation dynamics w…
Group-based Trajectory Modeling (GBTM) is applied to the citation curves of articles in six journals and to all citable items in a single field of science (Virology, 24 journals), in order to distinguish among the developmental trajectories…
The effect of stochasticity, in the form of Gaussian white noise, in a predator-prey model with two distinct time-scales is presented. A supercritical singular Hopf bifurcation yields a Type II excitability in the deterministic model. We…
We consider a finite or countable collection of one-dimensional Brownian particles whose dynamics at any point in time is determined by their rank in the entire particle system. Using Transportation Cost Inequalities for stochastic…
Einstein's explanation of Brownian motion provided one of the cornerstones which underlie the modern approaches to stochastic processes. His approach is based on a random walk picture and is valid for Markovian processes lacking long-term…
The characterization of the "most connected" nodes in static or slowly evolving complex networks has helped in understanding and predicting the behavior of social, biological, and technological networked systems, including their robustness…
We analyze the effect of additive fractional noise with Hurst parameter $H > \frac{1}{2}$ on fast-slow systems. Our strategy is based on sample paths estimates, similar to the approach by Berglund and Gentz in the Brownian motion case. Yet,…
The citations process for scientific papers has been studied extensively. But while the citations accrued by authors are the sum of the citations of their papers, translating the dynamics of citation accumulation from the paper to the…
In citation networks, the activity of papers usually decreases with age and dormant papers may be discovered and become fashionable again. To model this phenomenon, a competition mechanism is suggested which incorporates two factors:…
The main objective of the paper is to study the long-time behavior of general discrete dynamics driven by an ergodic stationary Gaussian noise. In our main result, we prove existence and uniqueness of the invariant distribution and exhibit…
Recently several authors have proposed stochastic evolutionary models for the growth of complex networks that give rise to power-law distributions. These models are based on the notion of preferential attachment leading to the ``rich get…
Entropy production in stochastic mechanical systems is examined here with strict bounds on its rate. Stochastic mechanical systems include pure diffusions in Euclidean space or on Lie groups, as well as systems evolving on phase space for…
Stochastic efficiency is evaluated in five case studies: driven Brownian motion, effusion with a thermo-chemical and thermo-velocity gradient, a quantum dot and a model for information to work conversion. The salient features of stochastic…
Mathematical models for complex systems are often accompanied with uncertainties. The goal of this paper is to extract a stochastic differential equation governing model with observation on stationary probability distributions. We develop a…
We investigate the asymptotic behavior of probability measures associated with stochastic dynamical systems featuring either globally contracting or $B_{r}$-contracting drift terms. While classical results often assume constant diffusion…
Our investigation is specially motivated by the stochastic version of a common model of potential spread in a dendritic tree. We do not assume the noise in the junction points to be Markovian. In fact, we allow for long-range dependence in…
Herein we develop a dynamical foundation for fractional Brownian Motion. A clear relation is established between the asymptotic behaviour of the correlation function and diffusion in a dynamical system. Then, assuming that scaling is…
We analyze the scaled voter model, which is a generalization of the noisy voter model with time-dependent herding behavior. We consider the case when the intensity of herding behavior grows as a power-law function of time. In this case, the…
We construct and study branching fractional Brownian motion with Hurst parameter $H\in(1/2,1)$. The construction relies on a generalization of the discrete approximation of fractional Brownian motion (Hammond and Sheffield, Probability…
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…
We demonstrate a comprehensive framework that accounts for citation dynamics of scientific papers and for the age distribution of references. We show that citation dynamics of scientific papers is nonlinear and this nonlinearity has…