Wilhelm Braun
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 |
Files
Braun_Thul_PRE_Jan_2017.pdf
(3.7 Mb)
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