If you place a large number of points randomly in the unit square, what is the distribution of
the radius of the largest circle containing no points? Of the smallest circle containing 4 …

The frequency stability of an optical frequency standard at 729 nm, based on a single
calcium ion, is numerically studied. It is investigated through the Allan deviation, whose …

We consider the problem of conditioning a continuous-time Markov chain (on a countably
infinite state space) not to hit an absorbing barrier before time T; and the weak convergence …

We study the behavior of random walk in random environment (RWRE) on trees in the
critical case left open in previous work. Representing the random walk by an electrical …

From both theoretical and applied perspectives, first passage time problems for random
processes are challenging and of great interest. In this thesis, our contribution consists on …

▶ Existence and uniqueness for ξ with no atoms (Chen, Cheng, et al. 2011, free boundary
problem)▶ Uniqueness (Ekström and Janson 2016, optimal stopping problem, see also …

Given a distribution on the positive extended real line, the two-sided inverse first-passage
time problem for Brownian motion asks for a function such that the first passage time of this …

The Hazard Rate Tangent Approximation for Boundary Hitting Times Page 1 The Annals of
Applied Probability 1995, Vol. 5, No. 2, 446-460 THE HAZARD RATE TANGENT …

Пусть задано распределение на расширенной положительной оси; двусторонняя
обратная задача о моменте первого пересечения для броуновского движения …

We consider the problem of conditioning a non-explosive birth and death process to remain
positive until time T, and consider weak convergence of this conditional process as T→∞ …