TY - JOUR T1 - Heavy-tailed distributions in a stochastic gene autoregulation model JF - bioRxiv DO - 10.1101/2021.06.02.446860 SP - 2021.06.02.446860 AU - Pavol Bokes Y1 - 2021/01/01 UR - http://biorxiv.org/content/early/2021/06/03/2021.06.02.446860.abstract N2 - Synthesis of gene products in bursts of multiple molecular copies is an important source of gene expression variability. This paper studies large deviations in a Markovian drift–jump process that combines exponentially distributed bursts with deterministic degradation. Large deviations occur as a cumulative effect of many bursts (as in diffusion) or, if the model includes negative feedback in burst size, in a single big jump. The latter possibility requires a modification in the WKB solution in the tail region. The main result of the paper is the construction, via a modified WKB scheme, of matched asymptotic approximations to the stationary distribution of the drift–jump process. The stationary distribution possesses a heavier tail than predicted by a routine application of the scheme.MSC 2020 92C40; 60J76, 45D05, 41A60Competing Interest StatementThe authors have declared no competing interest. ER -