Role of delay in the stochastic creation process.

We develop an approximate theoretical method to study discrete stochastic birth and death models that include a delay time. We analyze the effect of the delay in the fluctuations of the system and obtain that it can qualitatively alter them. We also study the effect of distributed delay. We apply the method to a protein-dynamics model that explicitly includes transcription and translation delays. The theoretical model allows us to understand in a general way the interplay between stochasticity and delay.

[1]  N. Kampen,et al.  Stochastic processes in physics and chemistry , 1981 .

[2]  S. Lowen.  The Biophysical Journal , 1960, Nature.

[3]  Carolyn Gibson,et al.  Genes and development. , 2011, European journal of oral sciences.

[4]  Current Biology , 2012, Current Biology.

[5]  R. Rosenfeld.  Nature , 2009, Otolaryngology--head and neck surgery : official journal of American Academy of Otolaryngology-Head and Neck Surgery.

[6]  John J. Tyson,et al.  Biochemical Oscillations , 2004 .

[7]  S. A. Dodds,et al.  Chemical Physics , 1877, Nature.

[8]  Peter C. Jurs,et al.  Mathematica , 2019, J. Chem. Inf. Comput. Sci..

[9]  W. Ebeling.  Stochastic Processes in Physics and Chemistry , 1995 .

[10]  Hal L. Smith,et al.  An introduction to delay differential equations with applications to the life sciences / Hal Smith , 2010 .

[11]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[12]  Steven E. Shreve,et al.  Stochastics and stochastics reports , 1990 .

[13]  D. Sherrington.  Stochastic Processes in Physics and Chemistry , 1983 .