Related papers: Cosmic Mass Functions from Gaussian Stochastic Dif…
Diffusion theory establishes a fundamental connection between stochastic differential equations and partial differential equations. The solution of a partial differential equation known as the Fokker-Planck equation describes the…
How and where cosmic rays are produced, and how they diffuse through various turbulent media, represent fundamental problems in astrophysics with far reaching implications, both in terms of our theoretical understanding of high-energy…
Obtaining a reduced description with particle and momentum flux densities outgoing from the microscopic equations of motion of the particles requires approximations. The usual method, we refer to as truncation method, is to zero Fourier…
Fields in cosmology, such as the matter distribution, are observed by experiments up to experimental noise. The first step in cosmological data analysis is usually to de-noise the observed field using an analytic or simulation driven prior.…
We present a generic framework to compute the one-point statistics of cosmological perturbations, when coarse-grained at an arbitrary scale $R$, in the presence of quantum diffusion. Making use of the stochastic-$\delta N$ formalism, we…
We compute the dark matter halo mass function using the excursion set formalism for a diffusive barrier with linearly drifting average which captures the main features of the ellipsoidal collapse model. We evaluate the non-Markovian…
The Gaussian Kinematic Formula (GKF, see Adler and Taylor (2007,2011)) is an extremely powerful tool allowing for explicit analytic predictions of expected values of Minkowski functionals under realistic experimental conditions for…
Complex behaviour in many systems arises from the stochastic interactions of spatially distributed particles or agents. Stochastic reaction-diffusion processes are widely used to model such behaviour in disciplines ranging from biology to…
Galactic diffuse emissions in gamma rays and neutrinos arise from interactions of cosmic rays with the interstellar medium and probe the cosmic-ray intensity away from the Solar system. Model predictions for those are influenced by the…
We study the galaxy cosmological mass function (GCMF) in a semi-empirical relativistic approach using observational data provided by galaxy redshift surveys. Starting from the theory of Ribeiro & Stoeger (2003, arXiv:astro-ph/0304094)…
We investigate numerical behaviour of a convection diffusion equation with random coefficients by approximating statistical moments of the solution. Stochastic Galerkin approach, turning the original stochastic problem to a system of…
Normalizing flows are a powerful tool to create flexible probability distributions with a wide range of potential applications in cosmology. Here we are studying normalizing flows which represent cosmological observables at field level,…
The analysis of space-time data from complex, real-life phenomena requires the use of flexible and physically motivated covariance functions. In most cases, it is not possible to explicitly solve the equations of motion for the fields or…
Aims. We aim to study the stochastic evolution of the smoothed overdensity $\delta$ at scale $S$ of the form $\delta(S) = \int_{0}^S K(S,u)\mathrm{d}W(u)$, where $K$ is a kernel and $\mathrm{d}W$ is the usual Wiener process. Methods. For a…
We propose a general method to identify nonlinear Fokker--Planck--Kolmogorov equations (FPK equations) as gradient flows on the space of probability measures on $\mathbb{R}^d$ with a natural differential geometry. Our notion of gradient…
We develop a stochastic formulation of cosmology in the early universe, after considering the scatter in the redshift-apparent magnitude diagram in the early epochs as an observational evidence for the non-deterministic evolution of early…
The application of Stochastic Differential Equations (SDEs) to the analysis of temporal data has attracted increasing attention, due to their ability to describe complex dynamics with physically interpretable equations. In this paper, we…
With the development of new remote sensing technology, large or even massive spatial datasets covering the globe become available. Statistical analysis of such data is challenging. This article proposes a semiparametric approach to model…
Stochastic processes associated with traveling wave solutions of the sine-Gordon equation are presented. The structure of the forward Kolmogorov equation as a conservation law is essential in the construction and so is the traveling wave…
A Gaussian operator basis provides a means to formulate phase-space simulations of the real- and imaginary-time evolution of quantum systems. Such simulations are guaranteed to be exact while the underlying distribution remains…