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The Poisson distribution arises naturally when dealing with data involving counts, and it has found many applications in inverse problems and imaging. In this work, we develop an approximate Bayesian inference technique based on expectation…
The probability density function (PDF) of a random variable associated with the solution of a partial differential equation (PDE) with random parameters is approximated using a truncated series expansion. The random PDE is solved using two…
Recently, there has been significant progress in the development of distributed first order methods. (At least) two different types of methods, designed from very different perspectives, have been proposed that achieve both exact and linear…
A large and sparse random graph with independent exponentially distributed link weights can be used to model the propagation of messages or diseases in a network with an unknown connectivity structure. In this article we study an extended…
We consider the exact path sampling of the squared Bessel process and some other continuous-time Markov processes, such as the CIR model, constant elasticity of variance diffusion model, and hypergeometric diffusions, which can all be…
The spatial distribution of galaxies is a highly complex phenomenon currently impossible to predict deterministically. However, by using a statistical $\textit{bias}$ relation, it becomes possible to robustly model the average abundance of…
The Fourier extension method, also known as the Fourier continuation method, is a method for approximating non-periodic functions on an interval using truncated Fourier series with period larger than the interval on which the function is…
In this work, we consider the numerical solution of an initial boundary value problem for the distributed order time fractional diffusion equation. The model arises in the mathematical modeling of ultra-slow diffusion processes observed in…
Master equations are common descriptions of mesoscopic systems. Analytical solutions to these equations can rarely be obtained. We here derive an analytical approximation of the time-dependent probability distribution of the master equation…
We explore first-passage phenomenology for biased active processes with a renewal-type structure, focusing in particular on paradigmatic run-and-tumble models in both discrete and continuous state spaces. In general, we show there is no…
For the special case of freely evolving Dirac electrons in $1 + 1$ dimensions, Feynman checkerboard paths have previously been used to derive Wigner's arrival-time distribution which includes all arrivals. Here, an attempt is made to use…
In this paper, we derive an integral representation for the density of the reciprocal of the first hitting time of the boundary of a wedge of angle $\pi/4$ by a radial Dunkl process with equal multiplicity values. Not only this…
Mixture transition distribution time series models build high-order dependence through a weighted combination of first-order transition densities for each one of a specified number of lags. We present a framework to construct stationary…
This article presents a new class of generalized transmuted lifetime distributions which includes a large number of lifetime distributions as sub-family. Several important mathematical quantities such as density function, distribution…
A random walk problem with particles on discrete double infinite linear grids is discussed. The model is based on the work of Montroll and others. A probability connected with the problem is given in the form of integrals containing…
This study aims at examination of the lower-order spectral moments in collision-induced absorption (CIA), taking the translational He-Ar band as an example. General quantum corrections for the zeroth and first spectral moments are derived…
Many of the important conclusions about Gamma-Ray Bursts follow from the distributions of various quantities such as peak flux or duration. We show that for astrophysical transients such as bursts, multiple selection thresholds can lead to…
We derive an approximate but fully explicit formula for the mean first-passage time (MFPT) to a small absorbing target of arbitrary shape in a general elongated domain in the plane. Our approximation combines conformal mapping, boundary…
A rapidly increasing number of systems is identified in which the stochastic motion of tracer particles follows the Brownian law $\langle\mathbf{r}^2(t) \rangle\simeq Dt$ yet the distribution of particle displacements is strongly…
We study the first-passage time (FPT) problem for widespread recurrent processes in confined though large systems and present a comprehensive framework for characterizing the FPT distribution over many time scales. We find that the FPT…