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Mean-field models are a popular tool in a variety of fields. They provide an understanding of the impact of interactions among a large number of particles or people or other "self-interested agents", and are an increasingly popular tool in…
We generalise the construction of multivariate Hawkes processes to a possibly infinite network of counting processes on a directed graph $\mathbb G$. The process is constructed as the solution to a system of Poisson driven stochastic…
Motivated by limits of critical inhomogeneous random graphs, we construct a family of sequences of measured metric spaces that we call continuous multiplicative graphs, that are expected to be the universal limit of graphs related to the…
The chaotic diffusion for a family of Hamiltonian mappings whose angles diverge in the limit of vanishingly action is investigated by using the solution of the diffusion equation. The system is described by a two-dimensional mapping for the…
We consider dynamics of the empirical measure of vertex neighborhood states of Markov interacting jump processes on sparse random graphs, in a suitable asymptotic limit as the graph size goes to infinity. Under the assumption of a certain…
An individual-based model of an infinite system of point particles in $\mathbb{R}^d$ is proposed and studied. In this model, each particle at random produces a finite number of new particles and disappears afterwards. The phase space for…
Motivated by some recent potential theoretic results on subordinate killed L\'evy processes in open subsets of the Euclidean space, we study processes in an open set $D\subset {\mathbb R}^d$ defined via Dirichlet forms with jump kernels of…
Note that the serial structure of blockchain has many essential pitfalls, thus a data network structure and its DAG-based blockchain are introduced to resolve the blockchain pitfalls. From such a network perspective, analysis of the…
We consider a class of piecewise-deterministic Markov processes where the state evolves according to a linear dynamical system. This continuous time evolution is interspersed by discrete events that occur at random times and change (reset)…
We study the estimation of the value function for continuous-time Markov diffusion processes using a single, discretely observed ergodic trajectory. Our work provides non-asymptotic statistical guarantees for the least-squares…
Continuous-time Markov chains describing interacting processes exhibit a state space that grows exponentially in the number of processes. This state-space explosion renders the computation or storage of the time-marginal distribution, which…
We consider two classes of natural stochastic processes on finite unlabeled graphs. These are Euclidean stochastic optimization algorithms on the adjacency matrix of weighted graphs and a modified version of the Metropolis MCMC algorithm on…
We prove an averaging principle which asserts convergence of diffusion processes on domains separated by semi-permeable membranes, when diffusion coefficients tend to infinity while the flux through the membranes remains constant. In the…
Let $\mu$ = ($\mu$t)t$\in$R be any 1-parameter family of probability measures on R. Its quantile process (Gt)t$\in$R : ]0, 1[ $\rightarrow$ RR, given by Gt($\alpha$) = inf{x $\in$ R : $\mu$t(]--$\infty$, x]) > $\alpha$}, is not Markov in…
We investigate toy dynamical models of energy-level repulsion in quantum eigenvalue sequences. We focus on parametric (with respect to a running coupling or "complexity" parameter) stochastic processes that are capable of relaxing towards a…
Many biological and medical questions can be modeled using time-to-event data in finite-state Markov chains, with the phase-type distribution describing intervals between events. We solve the inverse problem: given a phase-type…
In a series of works published in the 1990-s, Kerov put forth various applications of the circle of ideas centred at the Markov moment problem to the limiting shape of random continual diagrams arising in representation theory and spectral…
Many integrable stochastic particle systems in one space dimension (such as TASEP - totally asymmetric simple exclusion process - and its various deformations, with a notable exception of ASEP) remain integrable when we equip each particle…
Consider a filtering process associated to a hidden Markov model with densities for which both the state space and the observation space are complete, separable, metric spaces. If the underlying, hidden Markov chain is strongly ergodic and…
Designing mechanical linkages to achieve target end-effector trajectories presents a fundamental challenge due to the intricate coupling between continuous node placements, discrete topological configurations, and nonlinear kinematic…