Sign changes as a universal concept in first-passage-time calculationsTools 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 Full text not available from this repository.AbstractFirst-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.
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