Related papers: Approximating the first passage time density from …
This article describes a new Monte Carlo method for the evaluation of the orthant probabilities by sampling first passage times of a non-singular Gaussian discrete time-series across an absorbing boundary. This procedure makes use of a…
We give a highly efficient "semi-agnostic" algorithm for learning univariate probability distributions that are well approximated by piecewise polynomial density functions. Let $p$ be an arbitrary distribution over an interval $I$ which is…
A discrete-time totally asymmetric simple exclusion process on a lattice with open boundaries is considered. There are particles of different types. The type of a particle is characterized by the probability that a particle moves to a…
On the half line we introduce a new sequence of near--best uniform approximation polynomials, easily computable by the values of the approximated function at a truncated number of Laguerre zeros. Such approximation polynomials come from a…
In this paper we use an iterative algorithm for solving Fredholm equations of the first kind. The basic algorithm is known and is based on an EM algorithm when involved functions are non-negative and integrable. With this algorithm we…
We consider the problem of bounding mean first passage times for a class of continuous-time Markov chains that captures stochastic interactions between groups of identical agents. The quantitative analysis of such probabilistic population…
We develop a model to compute the first-passage time of a random walker in a crowded environment. Hard-core particles with the same size and diffusion coefficient than the tracer diffuse, and the model allows to compute the first passage…
In this paper we present a computation of the mean first-passage times both for a random walk in a discrete bounded lattice, between a starting site and a target site, and for a Brownian motion in a bounded domain, where the target is a…
We prove that for a standard Brownian motion, there exists a first-passage-time density function through a locally H\"older continuous curve with exponent greater than 1/2. By using a property of local time of a standard Brownian motion and…
We propose a data-driven method to learn the time-dependent probability density of a multivariate stochastic process from sample paths, assuming that the initial probability density is known and can be evaluated. Our method uses a novel…
The aim of this paper is to study the law of the last passage time of a linear diffusion to a curved boundary. We start by giving a general expression for the density of such a random variable under some regularity assumptions. Following…
The crucial step in designing a particle filter for a particular application is the choice of importance density. The optimal scheme is to use the conditional posterior density of the state, but this cannot be sampled or calculated…
Grouped data are commonly encountered in applications. The Bernstein polynomial model is proposed as an approximate model in this paper for estimating a univariate density function based on grouped data. The coefficients of the Bernstein…
We reconsider a nonparametric density model based on Gaussian processes. By augmenting the model with latent P\'olya--Gamma random variables and a latent marked Poisson process we obtain a new likelihood which is conjugate to the model's…
Recently developed particle flow algorithms provide an alternative to importance sampling for drawing particles from a posterior distribution, and a number of particle filters based on this principle have been proposed. Samples are drawn…
Gaussian time-series models are often specified through their spectral density. Such models present several computational challenges, in particular because of the non-sparse nature of the covariance matrix. We derive a fast approximation of…
The study of first passage times for diffusing particles reaching target states is foundational in various practical applications, including diffusion-controlled reactions. In this work, we present a bi-scaling theory for the probability…
Systems where resource availability approaches a critical threshold are common to many engineering and scientific applications and often necessitate the estimation of first passage time statistics of a Brownian motion (Bm) driven by…
Many scientific questions can be framed as asking for a first passage time (FPT), which generically describes the time it takes a random "searcher" to find a "target." The important timescale in a variety of biophysical systems is the time…
We study the first passage time (FPT) problem for biased continuous time random walks. Using the recently formulated framework of fractional Fokker-Planck equations, we obtain the Laplace transform of the FPT density function when the bias…