Sign changes as a universal concept in first-passage-time calculations
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...
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| Format: | Article |
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American Physical Society
2017
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| Online Access: | https://eprints.nottingham.ac.uk/39725/ |
| _version_ | 1848795898853720064 |
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| author | Braun, Wilhelm Thul, Ruediger |
| author_facet | Braun, Wilhelm Thul, Ruediger |
| author_sort | Braun, Wilhelm |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T19:39:24Z |
| format | Article |
| id | nottingham-39725 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:39:24Z |
| publishDate | 2017 |
| publisher | American Physical Society |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-397252020-05-04T18:31:16Z https://eprints.nottingham.ac.uk/39725/ Sign changes as a universal concept in first-passage-time calculations Braun, Wilhelm Thul, Ruediger 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. American Physical Society 2017-01-09 Article PeerReviewed Braun, Wilhelm and Thul, Ruediger (2017) Sign changes as a universal concept in first-passage-time calculations. Physical Review E, 95 (012114). pp. 1-7. ISSN 2470-0053 http://journals.aps.org/pre/abstract/10.1103/PhysRevE.95.012114 doi:10.1103/PhysRevE.95.012114 doi:10.1103/PhysRevE.95.012114 |
| spellingShingle | Braun, Wilhelm Thul, Ruediger Sign changes as a universal concept in first-passage-time calculations |
| title | Sign changes as a universal concept in first-passage-time calculations |
| title_full | Sign changes as a universal concept in first-passage-time calculations |
| title_fullStr | Sign changes as a universal concept in first-passage-time calculations |
| title_full_unstemmed | Sign changes as a universal concept in first-passage-time calculations |
| title_short | Sign changes as a universal concept in first-passage-time calculations |
| title_sort | sign changes as a universal concept in first-passage-time calculations |
| url | https://eprints.nottingham.ac.uk/39725/ https://eprints.nottingham.ac.uk/39725/ https://eprints.nottingham.ac.uk/39725/ |