19 research outputs found
Dynamic behavior of stochastic gene expression models in the presence of bursting
This paper considers the behavior of discrete and continuous mathematical
models for gene expression in the presence of transcriptional/translational
bursting. We treat this problem in generality with respect to the distribution
of the burst size as well as the frequency of bursting, and our results are
applicable to both inducible and repressible expression patterns in prokaryotes
and eukaryotes. We have given numerous examples of the applicability of our
results, especially in the experimentally observed situation that burst size is
geometrically or exponentially distributed.Comment: 22 page
Multiscale Systems, Homogenization, and Rough Paths:VAR75 2016: Probability and Analysis in Interacting Physical Systems
In recent years, substantial progress was made towards understanding
convergence of fast-slow deterministic systems to stochastic differential
equations. In contrast to more classical approaches, the assumptions on the
fast flow are very mild. We survey the origins of this theory and then revisit
and improve the analysis of Kelly-Melbourne [Ann. Probab. Volume 44, Number 1
(2016), 479-520], taking into account recent progress in -variation and
c\`adl\`ag rough path theory.Comment: 27 pages. Minor corrections. To appear in Proceedings of the
Conference in Honor of the 75th Birthday of S.R.S. Varadha
Diffusion and Deterministic Systems
We show that simple diffusion processes are weak limits of piecewise continuous processes
constructed within a totally deterministic framework. The proofs are based on the
continuous mapping theorem and the functional central limit theorem
Towards nonlinear cell population model structured by molecular content
International audienc