Related papers: Asymptotics for a Class of Self-Exciting Point Pro…
We introduce a new interacting particle system on $\mathbb{Z}$, \emph{slowed $t$-TASEP}. It may be viewed as a $q$-TASEP with additional position-dependent slowing of jump rates depending on a parameter $t$, which leads to discrete and…
We consider the task of learning individual-specific intensities of counting processes from a set of static variables and irregularly sampled time series. We introduce a novel modelization approach in which the intensity is the solution to…
This paper investigates the asymptotic behavior of higher-order conditional tail moments, which quantify the contribution of individual losses in the event of systemic collapse. The study is conducted within a framework comprising two…
We consider the stochastic ranking process with space-time dependent unbounded jump rates for the particles. We prove that the joint empirical distribution of jump rate and scaled position converges almost surely to a deterministic…
The activity patterns of highly developed cognitive systems like the human brain are dominated by autonomous dynamical processes, that is by a self-sustained activity which would be present even in the absence of external sensory stimuli.…
We analyzed the stochastic behavior of systems controlled by autocatalytic reaction A+X -> X+X. Assuming the distribution of reacting particles in the system volume to be uniform, we introduced the notion of the point model of reaction…
Point processes are becoming very popular in modeling asynchronous sequential data due to their sound mathematical foundation and strength in modeling a variety of real-world phenomena. Currently, they are often characterized via intensity…
Affine point processes are a class of simple point processes with self- and mutually-exciting properties, and they have found useful applications in several areas. In this paper, we obtain large-time asymptotic expansions in large…
Consider a branching Markov process, $X = (X(t), t \ge 0)$, with non-local branching mechanism. Studying the asymptotic behaviour of the moments of X has recently received attention in the literature [6, 7] due to the importance of these…
We introduce and show the existence of a Hawkes self-exciting point process with exponentially-decreasing kernel and where parameters are time-varying. The quantity of interest is defined as the integrated parameter…
Asymptotic equivalence in Le Cam's sense for nonparametric regression experiments is extended to the case of non-regular error densities, which have jump discontinuities at their endpoints. We prove asymptotic equivalence of such regression…
Extropy, a complementary dual of entropy, (proposed by Lad et al. \cite{lad2015extropy} in 2015) has attracted considerable interest from the research community. In this study, we focus on discrete random variables and define conditional…
Hawkes processes are a particularly interesting class of stochastic process that have been applied in diverse areas, from earthquake modelling to financial analysis. They are point processes whose defining characteristic is that they…
Hawkes point processes are first-order non-Markovian stochastic models of intermittent bursty dynamics with applications to physical, seismic, epidemic, biological, financial, and social systems. While accounting for positive feedback loops…
We consider a fully stochastic excitatory neuronal network with a number of subpopulations with different firing rates. We show that as network size goes to infinity, this limits on a deterministic hybrid model whose trajectories are…
Intermittent large amplitude events are seen in the temporal evolution of a state variable of many dynamical systems. Such intermittent large events suddenly start appearing in dynamical systems at a critical value of a system parameter and…
We study the asymptotic law of a network of interacting neurons when the number of neurons becomes infinite. The dynamics of the neurons is described by a set of stochastic differential equations in discrete time. The neurons interact…
We consider two independent random variables with the given tail asymptotic (e.g. power or exponential). We find tail asymptotic for their sum and product. This is done by some cumbersome but purely technical computations and requires the…
The paper analyses stochastic systems describing reacting molecular systems with a combination of two types of state spaces, a finite-dimensional, and an infinite dimenional part. As a typical situation consider the interaction of larger…
The study of density-dependent stochastic population processes is important from a historical perspective as well as from the perspective of a number of existing and emerging applications today. In more recent applications of these…