Convergence of stochastic gene networks to hybrid piecewise deterministic processes
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Ovidiu Radulescu | Arnaud Debussche | Alina Crudu | A. Debussche | O. Radulescu | A. Crudu | Aur'elie Muller | Aurelien Muller
[1] T. Kurtz. Strong approximation theorems for density dependent Markov chains , 1978 .
[2] A. Shiryaev,et al. Limit Theorems for Stochastic Processes , 1987 .
[3] J. Lygeros,et al. General stochastic hybrid systems: modelling and optimal control , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).
[4] M. Manhart,et al. Markov Processes , 2018, Introduction to Stochastic Processes and Simulation.
[5] Harold J. Kushner,et al. Approximation and Weak Convergence Methods for Random Processes , 1984 .
[6] P. R. ten Wolde,et al. Exact results for noise power spectra in linear biochemical reaction networks. , 2005, The Journal of chemical physics.
[7] S. Leibler,et al. Biological rhythms: Circadian clocks limited by noise , 2000, Nature.
[8] S Zeiser,et al. Simulation of genetic networks modelled by piecewise deterministic Markov processes. , 2008, IET systems biology.
[9] J. Paulsson. Summing up the noise in gene networks , 2004, Nature.
[10] S. Ethier,et al. Markov Processes: Characterization and Convergence , 2005 .
[11] Wilhelm Huisinga,et al. ADAPTIVE SIMULATION OF HYBRID STOCHASTIC AND DETERMINISTIC MODELS FOR BIOCHEMICAL SYSTEMS , 2005 .
[12] Arunabha Bagchi,et al. Modeling Stochastic Hybrid Systems , 2003, System Modelling and Optimization.
[13] N. Friedman,et al. Stochastic protein expression in individual cells at the single molecule level , 2006, Nature.
[14] Patrick Billingsley,et al. Weak convergence of measures - applications in probability , 1971, CBMS-NSF regional conference series in applied mathematics.
[15] John Lygeros,et al. Stochastic Hybrid Models: An Overview , 2003, ADHS.
[16] T. Kurtz. Limit theorems for sequences of jump Markov processes approximating ordinary differential processes , 1971, Journal of Applied Probability.
[17] Rajesh Sharma,et al. Asymptotic analysis , 1986 .
[18] A. Kierzek,et al. The Effect of Transcription and Translation Initiation Frequencies on the Stochastic Fluctuations in Prokaryotic Gene Expression* , 2001, The Journal of Biological Chemistry.
[19] Jerome T. Mettetal,et al. Heritable Stochastic Switching Revealed by Single-Cell Genealogy , 2007, PLoS biology.
[20] Aurélie Muller,et al. Théorèmes limites pour des processus de Markov à sauts. Synthèse des résultats et applications en biologie moleculaire , 2007 .
[21] D. Gillespie. A General Method for Numerically Simulating the Stochastic Time Evolution of Coupled Chemical Reactions , 1976 .
[22] J. Rawlings,et al. Approximate simulation of coupled fast and slow reactions for stochastic chemical kinetics , 2002 .
[23] Josselin Garnier,et al. Wave Propagation and Time Reversal in Randomly Layered Media , 2007 .
[24] Sandeep Krishna,et al. Stochastic simulations of the origins and implications of long-tailed distributions in gene expression. , 2005, Proceedings of the National Academy of Sciences of the United States of America.
[25] M. Delbrück. Statistical Fluctuations in Autocatalytic Reactions , 1940 .
[26] Onno Boxma,et al. ON/OFF STORAGE SYSTEMS WITH STATE-DEPENDENT INPUT, OUTPUT, AND SWITCHING RATES , 2005, Probability in the Engineering and Informational Sciences.
[27] T. Kepler,et al. Stochasticity in transcriptional regulation: origins, consequences, and mathematical representations. , 2001, Biophysical journal.
[28] Mark H. Davis. Markov Models and Optimization , 1995 .
[29] P. Billingsley,et al. Convergence of Probability Measures , 1969 .
[30] Alexander van Oudenaarden,et al. Stochastic Gene Expression: from Single Molecules to the Proteome This Review Comes from a Themed Issue on Chromosomes and Expression Mechanisms Edited Measuring Noise Mrna Fluctuations , 2022 .
[31] E. Giusti. Minimal surfaces and functions of bounded variation , 1977 .
[32] T. Elston,et al. Stochasticity in gene expression: from theories to phenotypes , 2005, Nature Reviews Genetics.
[33] Ovidiu Radulescu,et al. Théorèmes limites pour les processus de Markov à sauts , 2007, Tech. Sci. Informatiques.
[34] David Lindley,et al. CBMS-NSF REGIONAL CONFERENCE SERIES IN APPLIED MATHEMATICS , 2010 .
[35] Ovidiu Radulescu,et al. Hybrid stochastic simplifications for multiscale gene networks , 2009, BMC Systems Biology.
[36] T. Kurtz,et al. Submitted to the Annals of Applied Probability ASYMPTOTIC ANALYSIS OF MULTISCALE APPROXIMATIONS TO REACTION NETWORKS , 2022 .