Partner: R. Rudnicki

Ostatnie publikacje
1.Bobrowski A., Lipniacki T., Piechór K., Rudnicki R., Asymptotic behavior of distributions of mRNA and protein levels in a model of stochastic gene expression, JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, ISSN: 0022-247X, DOI: 10.1016/j.jmaa.2006.11.043, Vol.333, No.2, pp.753-769, 2007


The paper is devoted to a stochastic process introduced in the recent paper by Lipniacki et al. [T. Lipniacki, P. Paszek, A. Marciniak-Czochra, A.R. Brasier, M. Kimmel, Transcriptional stochasticity in gene expression, J. Theor. Biol. 238 (2006) 348–367] in modelling gene expression in eukaryotes. Starting from the full generator of the process we show that its distributions satisfy a (Fokker–Planck-type) system of partial differential equations. Then, we construct a c0 Markov semigroup in L1 space corresponding to this system. The main result of the paper is asymptotic stability of the involved semigroup in the set of densities.

Słowa kluczowe:

Piece-wise deterministic process, Stochastic gene expression, Semigroups of operators, Feller semigroups, Dual semigroups, Markov semigroups, Asymptotic stability

Afiliacje autorów:

Bobrowski A.-Lublin University of Technology (PL)
Lipniacki T.-IPPT PAN
Piechór K.-IPPT PAN
Rudnicki R.-other affiliation