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

Braun, Wilhelm; Thul, Ruediger

Authors

Wilhelm Braun

Ruediger Thul ruediger.thul@nottingham.ac.uk



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.

Journal Article Type Article
Publication Date Jan 9, 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
APA6 Citation Braun, W., & Thul, R. (2017). Sign changes as a universal concept in first-passage-time calculations. Physical Review E, 95(12114), doi:10.1103/PhysRevE.95.012114
DOI https://doi.org/10.1103/PhysRevE.95.012114
Publisher URL http://journals.aps.org/pre/abstract/10.1103/PhysRevE.95.012114
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





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