Related papers: Self-Exciting Random Evolutions (SEREs) and their …
The Hawkes self-excited point process provides an efficient representation of the bursty intermittent dynamics of many physical, biological, geological and economic systems. By expressing the probability for the next event per unit time…
Stochastic models for collections of interacting populations have crucial roles in scientific fields such as epidemiology and ecology, yet the standard approach to extending an ordinary differential equation model to a Markov chain does not…
Spike-sorting techniques attempt to classify a series of noisy electrical waveforms according to the identity of the neurons that generated them. Existing techniques perform this classification ignoring several properties of actual neurons…
We study a variant of the Generalized Excited Random Walk (GERW) on $\mathbb{Z}^d$ introduced by Menshikov, Popov, Ram\'irez and Vachkovskaia in [Ann. Probab. 40 (5), 2012]. It consists of a particular version of the model studied in [arXiv…
This paper is devoted to the study of a stochastic process obtained by random switching between a finite collection of vector fields. Such processes have recently been the focus of much attention in the case where the switching times are…
We present a class of SEIR Markov chain models for infectious diseases observed over discrete time in a random human population living in a closed environment. The population changes over time through random births, deaths, and transitions…
Masked language modeling, widely used in discriminative language model (e.g., BERT) pretraining, commonly adopts a random masking strategy. However, random masking does not consider the importance of the different words in the sentence…
Self-exciting processes of Hawkes type have been used to model various phenomena including earthquakes, neural activities, and views of online videos. Studies of temporal networks have revealed that sequences of social interevent times for…
We introduce and develop the concept of Maximal Entropy Random Walks (MERWs) on Weighted Bratteli Diagrams (WBDs), maximizing entropy production along paths as a natural criterion for choosing random walks on networks. Initially defined for…
The problem of making sequential decisions in unknown probabilistic environments is studied. In cycle $t$ action $y_t$ results in perception $x_t$ and reward $r_t$, where all quantities in general may depend on the complete history. The…
The rapid growth of social media has been witnessed during recent years as a result of the prevalence of the internet. This trend brings an increasing interest in simulating social media which can provide valuable insights to both academic…
In this paper, we introduce a new class of processes which are diffusions with jumps driven by a multivariate nonlinear Hawkes process. Our goal is to study their long-time behavior. In the case of exponential memory kernels for the…
Branching Processes in a Random Environment (BPREs) $(Z_n:n\geq0)$ are a generalization of Galton Watson processes where in each generation the reproduction law is picked randomly in an i.i.d. manner. We determine here the upper large…
We investigate a model of evolving random network, introduced by us previously {[}{\it Phys. Rev. Lett.} {\bf 83}, 5587 (1999){]} . The model is a generalization of the Bak-Sneppen model of biological evolution, with the modification that…
The number of extant individuals within a lineage, as exemplified by counts of species numbers across genera in a higher taxonomic category, is known to be a highly skewed distribution. Because the sublineages (such as genera in a clade)…
The self-avoiding random walk (SARW) is a stochastic process whose state variable avoids returning to previously visited states. This non-Markovian feature has turned SARWs a powerful tool for modelling a plethora of relevant aspects in…
Extreme-value theory for random vectors and stochastic processes with continuous trajectories is usually formulated for random objects all of whose univariate marginal distributions are identical. In the spirit of Sklar's theorem from…
We develop a stochastic human-rodent compartment model for Mpox transmission that combines diffusion noise with Hawkes self-exciting jumps in the human infection dynamics. Including Hawkes processes allows, for instance, to model the short…
We consider a sequence of Hawkes processes whose excitation measures may depend on the generation, and study its scaling limits in the near-unstable limiting regime. The limiting random measures, characterized via a nonlinear convolutional…
We study symmetric simple exclusion processes (SSEP) on a ring in the presence of uniformly moving multiple defects or disorders - a generalization of the model proposed earlier [Phys. Rev. E 89, 022138 (2014)]. The defects move with…