Related papers: Universal spectral features of different classes o…
We introduce a new class of nonparametric prior distributions on the space of continuously varying densities, induced by Dirichlet process mixtures which diffuse in time. These select time-indexed random functions without jumps, whose…
We study the existence of densities for distributions of piecewise deterministic Markov processes. We also obtain relationships between invariant densities of the continuous time process and that of the process observed at jump times. In…
Diffusion Models are probabilistic models that create realistic samples by simulating the diffusion process, gradually adding and removing noise from data. These models have gained popularity in domains such as image processing, speech…
In this paper we study the randomized non-autonomous complete linear differential equation. The diffusion coefficient and the source term in the differential equation are assumed to be stochastic processes and the initial condition is…
Brownian yet non-Gaussian phenomenon has recently been observed in many biological and active matter systems. The main idea of explaining this phenomenon is to introduce a random diffusivity for particles moving in inhomogeneous…
Non-Gaussianity indicates complex dynamics related to extreme events or significant outliers. However, the correlation between non-Gaussianity and the dynamics of heterogeneous environments in anomalous diffusion remains uncertain. Inspired…
We address the now classical problem of a diffusion process that crosses over from a ballistic behavior at short times to a fractional diffusion (sub- or super-diffusion) at longer times. Using the standard non-Markovian diffusion equation…
Representations based on random walks can exploit discrete data distributions for clustering and classification. We extend such representations from discrete to continuous distributions. Transition probabilities are now calculated using a…
In numerous applications data are observed at random times and an estimated graph of the spectral density may be relevant for characterizing and explaining phenomena. By using a wavelet analysis, one derives a nonparametric estimator of the…
We introduce a simple stochastic system able to generate anomalous diffusion both for position and velocity. The model represents a viable description of the Fermi's acceleration mechanism and it is amenable to analytical treatment through…
Numerical evidence of non-diffusive transport in three-dimensional, resistive pressure-gradient-driven plasma turbulence is presented. It is shown that the probability density function (pdf) of test particles' radial displacements is…
The transport equation of active motion is generalised to consider time-fractional dynamics for describing the anomalous diffusion of self-propelled particles observed in many different systems. In the present study, we consider an…
We propose a general framework for studying jump-diffusion systems driven by both Gaussian noise and a jump process with state-dependent intensity. Of particular natural interest are the jump locations: the system evaluated at the jump…
Diffusing-wave spectroscopy is a powerful technique which consists in measuring the temporal correlation function of the intensity of light multiply scattered by a medium. In this paper, we apply this technique to cold atoms under purely…
The motion of particles in random potentials occurs in several natural phenomena ranging from the mobility of organelles within a biological cell to the diffusion of stars within a galaxy. A Brownian particle moving in the random optical…
We suggest an explanation of typical incubation times statistical features based on the universal behavior of exit times for diffusion models. We give a mathematically rigorous proof of the characteristic right skewness of the incubation…
Diffusion probabilistic models have demonstrated an outstanding capability to model natural images and raw audio waveforms through a paired diffusion and reverse processes. The unique property of the reverse process (namely, eliminating…
The need for regression models to predict circular values arises in many scientific fields. In this work we explore a family of expressive and interpretable distributions over circle-valued random functions related to Gaussian processes…
We develop a class of non-Gaussian translation processes that extend classical stochastic differential equations (SDEs) by prescribing arbitrary absolutely continuous marginal distributions. Our approach uses a copula-based transformation…
We construct a class of one-dimensional diffusion processes on the particles of branching Brownian motion that are symmetric with respect to the limits of random martingale measures. These measures are associated with the extended extremal…