Sign changes as a universal concept in first-passage-time calculations

Braun, Wilhelm; Thul, Ruediger

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.

Citation

Braun, W., & Thul, R. (2017). Sign changes as a universal concept in first-passage-time calculations. Physical Review E, 95(12114), https://doi.org/10.1103/PhysRevE.95.012114

• Journal Article Type: Article
• Acceptance Date: Dec 23, 2016
• Publication Date: Jan 9, 2017
• Deposit Date: Jan 11, 2017
• Publicly Available Date: Jan 11, 2017
• Journal: Physical Review E
• Print ISSN: 2470-0045
• Electronic ISSN: 2470-0053
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 95
• Issue: 12114
• DOI: https://doi.org/10.1103/PhysRevE.95.012114
• Public URL: https://nottingham-repository.worktribe.com/output/841146
• Publisher URL: http://journals.aps.org/pre/abstract/10.1103/PhysRevE.95.012114
• Contract Date: Jan 11, 2017