Related papers: Likelihood theory for the Graph Ornstein-Uhlenbeck…
We study high-dimensional Ornstein--Uhlenbeck processes driven by L\'evy noise and consider drift matrices that decompose into a low-rank plus sparse component, capturing a few latent factors together with a sparse network of direct…
Randomising networks using a naive `accept-all' edge-swap algorithm is generally biased. Building on recent results for nondirected graphs, we construct an ergodic detailed balance Markov chain with non-trivial acceptance probabilities for…
We consider transport over a strongly connected, directed graph. The scheduling amounts to selecting transition probabilities for a discrete-time Markov evolution which is designed to be consistent with certain initial and final marginals.…
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…
We study random graphs with latent geometric structure, where the probability of each edge depends on the underlying random positions corresponding to the two endpoints. We focus on the setting where this conditional probability is a…
The on-line nearest-neighbour graph on a sequence of $n$ uniform random points in $(0,1)^d$ ($d \in \N$) joins each point after the first to its nearest neighbour amongst its predecessors. For the total power-weighted edge-length of this…
We consider a reflected Ornstein-Uhlenbeck process $X$ driven by a fractional Brownian motion with Hurst parameter $H\in (0, \frac12) \cup (\frac12, 1)$. Our goal is to estimate an unknown drift parameter $\alpha\in (-\infty,\infty)$ on the…
Growth-fragmentation processes describe systems of particles in which each particle may grow larger or smaller, and divide into smaller ones as time proceeds. Unlike previous studies, which have focused mainly on the self-similar case, we…
Dynamic network data analysis requires joint modelling individual snapshots and time dynamics. This paper proposes a new two-way heterogeneity model towards this goal. The new model equips each node of the network with two heterogeneity…
For an arbitrary Hilbert space-valued Ornstein-Uhlenbeck process we construct the Ornstein-Uhlenbeck Bridge connecting a starting point $x$ and an endpoint $y$ that belongs to a certain linear subspace of full measure. We derive also a…
In this paper we investigate the numerical approximation of an analogue of the Wasserstein distance for optimal transport on graphs that is defined via a discrete modification of the Benamou--Brenier formula. This approach involves the…
Starting from the notion of multivariate fractional Brownian Motion introduced in [F. Lavancier, A. Philippe, and D. Surgailis. Covariance function of vector self-similar processes. Statistics & Probability Letters, 2009] we define a…
The concept of a random process has been recently extended to graph signals, whereby random graph processes are a class of multivariate stochastic processes whose coefficients are matrices with a \textit{graph-topological} structure. The…
We study a generalization of the Brownian bridge as a stochastic process that models the position and velocity of inertial particles between the two end-points of a time interval. The particles experience random acceleration and are assumed…
We revisit the Ornstein-Uhlenbeck (OU) process as the fundamental mathematical description of linear irreversible phenomena, with fluctuations, near an equilibrium. By identifying the underlying circulating dynamics in a stationary process…
We consider Ornstein-Uhlenbeck processes (OU-processes) associated to hypoelliptic diffusion processes on finite-dimensional Lie groups: let $ \mathcal{L} $ be a hypoelliptic, left-invariant ``sum of the squares''-operator on a Lie group $…
In this paper, we investigate the parameter estimation for threshold Ornstein$\mathit{-}$Uhlenbeck processes. Least squares method is used to obtain continuous-type and discrete-type estimators for the drift parameters based on continuous…
We establish a diffusion approximation for a class of multi-agent controlled queueing systems, demonstrating their convergence to a system of interacting reflected Ornstein--Uhlenbeck (OU) processes. The limiting process captures essential…
We develop the generalized method of moments (GMM) estimation for the parameters of the finitely mixed multi-mixed fractional Ornstein--Uhlenbeck (mmfOU) processes, and analyze the consistency and asymptotic normality of this estimator. We…
We study the ergodic properties of a class of multidimensional piecewise Ornstein-Uhlenbeck processes with jumps, which contains the limit of the queueing processes arising in multiclass many-server queues with heavy-tailed arrivals and/or…