title: Sign changes as a universal concept in first-passage-time calculations.
abstract: First-passage-time problems are ubiquitous across many fields of study, including transport processes in semiconductors and biological synapses, evolutionary game theory and percolation. Despite their prominence, first-passage-time calculations have proven to be particularly challenging. Analytical results to date have often been obtained under strong conditions, leaving most of the exploration of first-passage-time problems to direct numerical computations. Here we present an analytical approach that allows the derivation of first-passage-time distributions for the wide class of nondifferentiable Gaussian processes. We demonstrate that the concept of sign changes naturally generalizes the common practice of counting crossings to determine first-passage events. Our method works across a wide range of time-dependent boundaries and noise strengths, thus alleviating common hurdles in first-passage-time calculations.
authors.affiliation: Department of Physics and Centre for Neural Dynamics, University of Ottawa, Ottawa, Canada K1N 6N5.
authors.forename: Wilhelm
authors.initials: W
authors.lastname: Braun
authors.affiliation: Centre for Mathematical Medicine and Biology, School of Mathematical Sciences, University of Nottingham, Nottingham, NG7 2RD, United Kingdom.
authors.forename: Rüdiger
authors.initials: R
authors.lastname: Thul