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We investigate the convergence in distribution of sequential empirical processes of dependent data indexed by a class of functions F. Our technique is suitable for processes that satisfy a multiple mixing condition on a space of functions…
In this paper we propose a class of propagation models for multiple competing products over a social network. We consider two propagation mechanisms: social conversion and self conversion, corresponding, respectively, to endogenous and…
The dynamics of many epidemic compartmental models for infectious diseases that spread in a single host population present a second-order phase transition. This transition occurs as a function of the infectivity parameter, from the absence…
An important problem arising in the study of complex networks, for instance in community detection and motif finding, is the sampling of graphs with fixed degree sequence. The equivalent problem of generating random 0,1 matrices with fixed…
Consider $ m $ copies of an irreducible, aperiodic Markov chain $ Y $ taking values in a finite state space. The asymptotics as $ m $ tends to infinity, of the first time from which on the trajectories of the $ m $ copies differ, have been…
Though widely used in applications, reinforced random walk on graphs have never been the subject of a valid statistical inference. We develop in this paper a statistical framework for a general two-colored urn model. The probability to draw…
We study an interacting particle system in which moving particles activate dormant particles linked by the components of critical bond percolation. Addressing a conjecture from Beckman, Dinan, Durrett, Huo, and Junge for a continuous…
We consider an infinite-dimensional stochastic clustering model on $\mathbb{R}$. In discrete time, each point of a unit-intensity simple point process moves halfway toward either of its left or right neighbors, chosen uniformly at random.…
In many dynamical systems in nature, the law of the dynamics changes along with the temporal evolution of the system. These changes are often associated with the occurrence of certain events. The timing of occurrence of these events…
Large deviation results are given for a class of perturbed nonhomogeneous Markov chains on finite state space which formally includes some stochastic optimization algorithms. Specifically, let {P_n} be a sequence of transition matrices on a…
We propose a rumor propagation model in which individuals within a homogeneously mixed population can assume one of infinitely many possible states. To analyze this model, we extend the classical law of large numbers for density-dependent…
The problem of graphical model selection is to correctly estimate the graph structure of a Markov random field given samples from the underlying distribution. We analyze the information-theoretic limitations of the problem of graph…
In this paper we establish a diffusion limit for a multivariate continuous time Markov chain whose components are indexed by vertices of a finite graph. The components take values in a common finite set of non-negative integers and evolve…
In this paper, we study the averaging principle and central limit theorem for multi-scale stochastic differential equations with state-dependent switching. To accomplish this, we first study the Poisson equation associated with a Markov…
We consider a continuous-time financial market with an asset whose price is modeled by a linear stochastic differential equation with drift and volatility switching driven by a uniformly ergodic jump Markov process with a countable state…
Systems of interacting continuous-time Markov chains are a powerful model class, but inference is typically intractable in high dimensional settings. Auxiliary information, such as noisy observations, is typically only available at discrete…
The Importance Markov chain is a novel algorithm bridging the gap between rejection sampling and importance sampling, moving from one to the other through a tuning parameter. Based on a modified sample of an instrumental Markov chain…
Ordinary differential equations obtained as limits of Markov processes appear in many settings. They may arise by scaling large systems, or by averaging rapidly fluctuating systems, or in systems involving multiple time-scales, by a…
We study the fragmentation-coagulation (or merging and splitting) evolutionary control model as introduced recently by one of the authors, where $N$ small players can form coalitions to resist to the pressure exerted by the principal. It is…
Dynamic networks exhibit temporal patterns that vary across different time scales, all of which can potentially affect processes that take place on the network. However, most data-driven approaches used to model time-varying networks…