2018/04/16 by Yuri Bakhtin, Bakhtin, Yuri
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #60J70 #91E #92D #Complex Network Analysis Techniques #FOS: Biological sciences #Opinion Dynamics and Social Influence #Quantitative Methods (q-bio.QM) #Stochastic processes and statistical mechanics #msc:60J70 #msc:91E #msc:92D #q-bio.QM
paper · pdf · doi:10.48550/arxiv.1804.05961
24 pages, 4 figures
arxiv created 2018/04/16 · openalex publication_date 2018/04/16 · arxiv updated 2018/04/18 · openalex created_date 2018/04/24 · openalex updated_date 2026/07/28
We suggest an explanation of typical incubation times statistical features based on the universal behavior of exit times for diffusion models. We give a mathematically rigorous proof of the characteristic right skewness of the incubation time distribution for very general one-dimensional diffusion models. Imposing natural simple conditions on the drift coefficient, we also study these diffusion models under the assumption of noise smallness and show that the limiting exit time distributions in the limit of vanishing noise are Gaussian and Gumbel. Thus they match the existing data as well as the other existing models do. The character of our models, however, allows us to argue that the features of the exit time distributions that we describe are universal and manifest themselves in various other situations where the times involved can be described as detection or halting times, for example, response times studied in psychology.