Instytut Podstawowych Problemów Techniki
Polskiej Akademii Nauk

Partnerzy

prof. dr hab. Ryszard Rudnicki

Institute of Mathematics, Polish Academy of Sciences (PL)

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

Streszczenie:
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. - Institute of Mathematics, Polish Academy of Sciences (PL)

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