Related papers: A localized coupling approach to interacting conti…
This study in centered on models accounting for stochastic deformations of sample paths of random walks, embedded either in $\mathbb{Z}^2$ or in $\mathbb{Z}^3$. These models are immersed in multi-type particle systems with exclusion.…
We study a density-dependent Markov jump process describing a population where each individual is characterized by a type, and reproduces at rates depending both on its type and on the population type distribution. We are interested in the…
We introduce a class of quantum Markov semigroups describing the evolution of interacting quantum lattice systems, specified either as generic qudits or as fermions. The corresponding generators, which include both conservative and…
We are interested in the dynamic of a structured branching population where the trait of each individual moves according to a Markov process. The rate of division of each individual is a function of its trait and when a branching event…
Focusing on stochastic systems arising in mean-field models, the systems under consideration belong to the class of switching diffusions, in which continuous dynamics and discrete events coexist and interact. The discrete events are modeled…
We propose an extension to Hawkes processes by treating the levels of self-excitation as a stochastic differential equation. Our new point process allows better approximation in application domains where events and intensities accelerate…
Dynamics on networks is considered from the perspective of Markov stochastic processes. We partially describe the state of the system through network motifs and infer any missing data using the available information. This versatile approach…
We consider a Markov jump process on a general state space to which we apply a time-dependent weak perturbation over a finite time interval. By martingale-based stochastic calculus, under a suitable exponential moment bound for the…
We examine entanglement dynamics via concurrence among four two-state systems labeled $A, ~a, ~B, ~b$. The four systems are arranged on an addressable "lattice" in such a way that $A$ and $a$ at one location labeled $Aa$ can interact with…
This paper uses two new ingredients, namely stochastic differential equations satisfied by continuous-state branching processes (CSBPs), and a topology under which the Lamperti transformation is continuous, in order to provide…
There has been a growing interest in studying online stochastic packing under more general correlation structures, motivated by the complex data sets and models driving modern applications. Several past works either assume correlations are…
We translate a coagulation-framentation model, describing the dynamics of animal group size distributions, into a model for the population distribution and associate the \blue{nonlinear} evolution equation with a Markov jump process of a…
We consider a system of particles which interact through a jump process. The jump intensities are functions of the proximity rank of the particles, a type of interaction referred to as topological in the literature. Such interactions have…
The study of time-inhomogeneous Markov jump processes is a traditional topic within probability theory that has recently attracted substantial attention in various applications. However, their flexibility also incurs a substantial…
We consider a system consisting of a planar random walk on a square lattice, submitted to stochastic elementary local deformations. Depending on the deformation transition rates, and specifically on a parameter $\eta$ which breaks the…
It is well-known from the work of Sch\"onbucher (2005) that the marginal laws of a loss process can be matched by a unit increasing time inhomogeneous Markov process, whose deterministic jump intensity is called local intensity. The…
We present properties of Lotka-Volterra equations describing ecological competition among a large number of competing species. First we extend to the case of a non-homogeneous niche space stability conditions for solutions representing…
This paper considers differential problems with random switching, with specific applications to the motion of cells and centrally coordinated motion. Starting with a differential-equation model of cell motion that was proposed previously,…
We present a general approach to model an integrated source of counterpropagating continuous-variable entangled states based on a coupled-resonator optical waveguide that is pumped by a classical pulsed source incident from above the…
We study a model of an infinite system of point particles in $\mathds{R}^d$ performing random jumps with attraction. The system's states are probability measures on the space of particle configurations, and their evolution is described by…