Related papers: On the connection between orthant probabilities an…

We derive an approximate formula for the mean first-passage time (MFPT) to a small absorbing target of arbitrary shape inside an elongated domain of a slowly varying axisymmetric profile. For this purpose, the original Poisson equation in…

In this paper, we consider a classic problem concerning the high excursion probabilities of a Gaussian random field $f$ living on a compact set $T$. We develop efficient computational methods for the tail probabilities $P(\sup_T f(t) > b)$…

A novel first-order autoregressive moving average model for analyzing discrete-time series observed at irregularly spaced times is introduced. Under Gaussianity, it is established that the model is strictly stationary and ergodic. In the…

First passage of stochastic processes under resetting has recently been an active research topic in the field of statistical physics. However, most of previous studies mainly focused on the systems with continuous time and space. In this…

We develop a theoretical framework for studying numerical estimation of lower previsions, generally applicable to two-level Monte Carlo methods, importance sampling methods, and a wide range of other sampling methods one might devise. We…

In this paper we consider parameter estimation for discretely observed diffusion processes. In particular, we focus on data that are observed at low frequency and methodology that can estimate parameters with uncertainty quantification.…

Safety evaluation of self-driving technologies has been extensively studied. One recent approach uses Monte Carlo based evaluation to estimate the occurrence probabilities of safety-critical events as safety measures. These Monte Carlo…

The time to first crossing for the Poisson counting process with respect to a linear moving barrier with offset is a classic problem, although key results remain scattered across the literature and their equivalence is often unclear. Here…

In this paper we extend results of L.A. Shepp by finding explicit formulas for the first passage probability $F_{a,b}(T\, |\, x)={\rm Pr}(S(t)<a+bt \text{ for all } t\in[0,T]\,\, | \,\,S(0)=x)$, for all $T>0$, where $S(t)$ is a Gaussian…

We present an algorithm to efficiently sample first-passage times for fractional Brownian motion. To increase the resolution, an initial coarse lattice is successively refined close to the target, by adding exactly sampled midpoints, where…

This article introduces two techniques for computing the distribution of the absorption or first passage time of the drifted Wiener diffusion subject to Poisson resetting times, to an upper hard wall barrier and to a lower absorbing…

In Monte Carlo simulations, proposed configurations are accepted or rejected according to an acceptance ratio, which depends on an underlying probability distribution and an a priori sampling probability. By carefully selecting the…

Hamiltonian Monte Carlo has emerged as a standard tool for posterior computation. In this article, we present an extension that can efficiently explore target distributions with discontinuous densities. Our extension in particular enables…

The main purpose of percolation theory is to model phase transitions in a variety of random systems, which is highly valuable in fields related to materials physics, biology, or otherwise unrelated areas like oil extraction or even quantum…

We present a Hamiltonian Monte Carlo algorithm to sample from multivariate Gaussian distributions in which the target space is constrained by linear and quadratic inequalities or products thereof. The Hamiltonian equations of motion can be…

A popular method to compute first-passage probabilities in continuous-time Markov chains is by numerically inverting their Laplace transforms. Past decades, the scientific computing community has developed excellent numerical methods for…

Sequential Monte Carlo methods which involve sequential importance sampling and resampling are shown to provide a versatile approach to computing probabilities of rare events. By making use of martingale representations of the sequential…

The main challenges that arise when adopting Gaussian Process priors in probabilistic modeling are how to carry out exact Bayesian inference and how to account for uncertainty on model parameters when making model-based predictions on…

First passage under restart has recently emerged as a conceptual framework to study various stochastic processes under restart mechanism. Emanating from the canonical diffusion problem by Evans and Majumdar, restart has been shown to…

We propose an approach for estimating the probability that a given small target, among many, will be the first to be reached in a molecular dynamics simulation. Reaching small targets out of a vast number of possible configurations…