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 non-differentiable Gaussian processes. We demonstrate that the concept of sign changes naturally generalises 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.

arXiv comment7 pages, 6 figures. Accepted for publication in Phys. Rev. E

References in corpus (17)

• Power laws, Pareto distributions and Zipf's law
• Diffusion with Stochastic Resetting
• Persistence and First-Passage Properties in Non-equilibrium Systems
• Optimal stochastic restart renders fluctuations in first passage times universal
• First-passage times for random walks in bounded domains
• Mean first-passage times of non-Markovian random walkers in confinement
• Vertical transmission of culture and the distribution of family names
• Ion channel gating: a first passage time analysis of the Kramers type
• First Passage Time Densities in Resonate-and-Fire Models
• Weighted Kolmogorov-Smirnov test: Accounting for the tails
• Switching Time Statistics for Driven Neuron Models: Analytic Expressions versus Numerics
• A phase transition in the first passage of a Brownian process through a fluctuating boundary: implications for neural coding
• Survival probability and first-passage-time statistics of a Wiener process driven by an exponential time-dependent drift
• First passage times in integrate-and-fire neurons with stochastic thresholds
• First-passage time to clear the way for receptor-ligand binding in a crowded environment
• Survival probability of a diffusing particle constrained by two moving, absorbing boundaries
• Approximation of the first passage time density of a Wiener process to an exponentially decaying threshold by two-piecewise linear threshold. Application to neuronal spiking activity