Related papers: Persistence of a Continuous Stochastic Process wit…
A system of $N$ particles in a chemical medium in $\mathbb{R}^{d}$ is studied in a discrete time setting. Underlying interacting particle system in continuous time can be expressed as \begin{eqnarray} dX_{i}(t) &=&[-(I-A)X_{i}(t) +…
In this paper, we analyze the dynamics of spreading processes taking place over time-varying networks. A common approach to model time-varying networks is via Markovian random graph processes. This modeling approach presents the following…
We consider the inverse problem of reconstructing the posterior measure over the trajec- tories of a diffusion process from discrete time observations and continuous time constraints. We cast the problem in a Bayesian framework and derive…
The problem of a diffusing particle moving among diffusing traps is analyzed in general space dimension d. We consider the case where the traps are initially randomly distributed in space, with uniform density rho, and derive upper and…
In this paper we consider parameter estimation for discretely observed diffusion processes. In particular, we focus on data that are observed at low frequency and methodology that can estimate parameters with uncertainty quantification.…
With $\{\xi_i\}_{i\ge 0}$ being a centered stationary Gaussian sequence with non-negative correlation function $\rho(i):=\mathbb{E}[ \xi_0\xi_i]$ and $\{\sigma(i)\}_{i\ge 1}$ a sequence of positive reals, we study the asymptotics of the…
The path probability of stochastic motion of non dissipative or quasi-Hamiltonian systems is investigated by numerical experiment. The simulation model generates ideal one-dimensional motion of particles subject only to conservative forces…
Discrete flow models offer a powerful framework for learning distributions over discrete state spaces and have demonstrated superior performance compared to the discrete diffusion models. However, their convergence properties and error…
The waiting time distribution (WTD) is a common tool for analysing discrete stochastic processes in classical and quantum systems. However, there are many physical examples where the dynamics is continuous and only approximately discrete,…
The smoothing distribution is the conditional distribution of the diffusion process in the space of trajectories given noisy observations made continuously in time. It is generally difficult to sample from this distribution. We use the…
We analyse the problem of stability of a continuous time linear switching system (LSS) versus the stability of its Euler discretization. It is well-known that the existence of a positive {\tau} for which the corresponding discrete time…
Diffusion models, which convert noise into new data instances by learning to reverse a Markov diffusion process, have become a cornerstone in contemporary generative modeling. While their practical power has now been widely recognized, the…
The persistence exponent, which characterises the long-time decay of the survival probability of stochastic processes in the presence of an absorbing target, plays a key role in quantifying the dynamics of fluctuating systems. Determining…
This work deals with the stability analysis of nonlinear sampled-data systems under nonuniform sampling. It establishes novel relationships between the stability property of the exact discrete-time model for a given sequence of (aperiodic)…
We study the discrete-time threshold-$\theta \geq 2$ contact process on random graphs of general degrees. For random graphs with a given degree distribution $\mu$, we show that if $\mu$ is lower bounded by $\theta+2$ and has finite $k$th…
We study the probabilistic behavior of persistence-based statistics and propose a novel nonparametric framework for detecting structural changes in high-dimensional random point clouds. We establish moment bounds and tightness results for…
We study the stochastic motion of active particles that undergo spontaneous transitions between two distinct modes of motion. Each mode is characterized by a velocity distribution and an arbitrary (anti-)persistence. We present an…
We consider the problem of nonparametric estimation of the drift and diffusion coefficients of a Stochastic Differential Equation (SDE), based on $n$ independent replicates $\left\{X_i(t)\::\: t\in [0,1]\right\}_{1 \leq i \leq n}$, observed…
Time delay in general leads to instability in some systems, while a specific feedback with delay can control fluctuated motion in nonlinear deterministic systems to a stable state. In this paper, we consider a non-stationary stochastic…
The motion of self-propelled particles is modeled as a persistent random walk. An analytical framework is developed that allows the derivation of exact expressions for the time evolution of arbitrary moments of the persistent walk's…