Related papers: Estimating migration proportions from discretely o…
While the overarching pattern of biannual avian migration is well understood, there are significant questions pertaining to this phenomenon that invite further study. Necessary to any analysis of these questions is an understanding of how a…
We study the diffusion of a particle with a time-dependent diffusion constant $D(t)$ that switches between random values drawn from a distribution $W(D)$ at a fixed rate $r$. Using a renewal approach, we compute exactly the moments of the…
Diffusion models simulate the propagation of influence in networks. The design and evaluation of diffusion models has been subjective and empirical. When being applied to a network represented by a graph, the diffusion model generates a…
In this paper a new dissimilarity measure to identify groups of assets dynamics is proposed. The underlying generating process is assumed to be a diffusion process solution of stochastic differential equations and observed at discrete time.…
Complex systems are characterized by a huge number of degrees of freedom often interacting in a non-linear manner. In many cases macroscopic states, however, can be characterized by a small number of order parameters that obey stochastic…
This paper considers the issue of modeling fractional data observed in the interval [0,1), (0,1] or [0,1]. Mixed continuous-discrete distributions are proposed. The beta distribution is used to describe the continuous component of the model…
This work aims at making a comprehensive contribution in the general area of parametric inference for discretely observed diffusion processes. Established approaches for likelihood-based estimation invoke a time-discretisation scheme for…
Diffusion models, a powerful and universal generative AI technology, have achieved tremendous success in computer vision, audio, reinforcement learning, and computational biology. In these applications, diffusion models provide flexible…
Typical generative diffusion models rely on a Gaussian diffusion process for training the backward transformations, which can then be used to generate samples from Gaussian noise. However, real world data often takes place in discrete-state…
Motivated by the task of computing normalizing constants and importance sampling in high dimensions, we study the dimension dependence of fluctuations for additive functionals of time-inhomogeneous Langevin-type diffusions on…
Many real-world systems modeled using partial differential equations (PDEs) involve unknown parameters that must be estimated from limited, noisy system observations. While typically assumed to be constants, some of these unobserved…
Multivariate Hawkes Processes (MHPs) are an important class of temporal point processes that have enabled key advances in understanding and predicting social information systems. However, due to their complex modeling of temporal…
Continuous time random walks are non-Markovian stochastic processes, which are only partly characterized by single-time probability distributions. We derive a closed evolution equation for joint two-point probability density functions of a…
This paper studies spatial patterns formed by proximate population migration driven by real wage gradients and other idiosyncratic factors. The model consists of a tractable core-periphery model incorporating a quasi-linear log utility…
Real data are constrained to finite sampling rates, which calls for a suitable mathematical description of the corrections to the finite-time estimations of the dynamic equations. Often in the literature, lower order discrete time…
In this work we propose a novel space-dependent multiscale model for the spread of infectious diseases in a two-dimensional spatial context on realistic geographical scenarios. The model couples a system of kinetic transport equations…
Linear diffusions are used to model a large number of stochastic processes in physics, including small mechanical and electrical systems perturbed by thermal noise, as well as Brownian particles controlled by electrical and optical forces.…
Quantifying how spatial disorder affects the movement of a diffusing particle or agent is fundamental to target search studies. When diffusion occurs on a network, that is on a highly disordered environment, we lack the mathematical tools…
In this paper we study some mathematical models describing evolution of population density and spread of epidemics in population systems in which spatial movement of individuals depends only on the departure and arrival locations and does…
We consider a one-dimensional diffusion process $(X_t)$ which is observed at $n+1$ discrete times with regular sampling interval $\Delta$. Assuming that $(X_t)$ is strictly stationary, we propose nonparametric estimators of the drift and…