Open Access
Issue
ESAIM: PS
Volume 25, 2021
Page(s) 258 - 285
DOI https://doi.org/10.1051/ps/2021008
Published online 04 June 2021
  1. F. Baccelli, D.R. Mcdonald and J. Reynier, A mean-field model for multiple TCP connections through a buffer implementing red. TREC (2002). [Google Scholar]
  2. H.T. Banks, K.L. Sutton, W. Clayton Thompson, G. Bocharov, D. Roose, T. Schenkel and A. Meyerhans, Estimation of cell proliferation dynamics using CFSE data. Bull. Math. Biol. 73 (2011) 116–150. [Google Scholar]
  3. V. Bansaye, B. Cloez and P. Gabriel, Ergodic behavior of non-conservative semigroups via generalized Doeblin’s conditions. Acta Appl. Math. 166 (2020) 29–72. [Google Scholar]
  4. V. Bansaye, B. Cloez, P. Gabriel and A. Marguet, A non-conservative Harris’ ergodic theorem. Preprint arXiv:1903.03946 (2019). [Google Scholar]
  5. J.-B. Bardet, A. Christen, A. Guillin, F. Malrieu and P.-A. Zitt, Total variation estimates for the TCP process. Electr. J. Probab. 18 (2013) 21. [Google Scholar]
  6. G.I. Bell and E.C. Anderson, Cell growth and division: I. A mathematical model with applications to cell volume distributions in mammalian suspension cultures. Biophys. J. 7 (1967) 329–351. [Google Scholar]
  7. E. Bernard and P. Gabriel, Asymptotic behavior of the growth-fragmentation equation with bounded fragmentation rate. J. Funct. Anal. 272 (2017) 3455–3485. [Google Scholar]
  8. J. Bertoin, On a Feynman-Kac approach to growth-fragmentation semigroups and their asymptotic behaviors. J. Functional Anal. (2019). [Google Scholar]
  9. J. Bertoin and A.R. Watson, Probabilistic aspects of critical growth-fragmentation equations. Adv. Appl. Probab. 48 (2016) 37–61. [Google Scholar]
  10. J. Bertoin and A.R. Watson, A probabilistic approach to spectral analysis of growth-fragmentation equations. J. Funct. Anal. 274 (2018) 2163–2204. [Google Scholar]
  11. F. Bouguet, A probabilistic look at conservative growth-fragmentation equations, in Séminaire de Probabilités XLIX. Vol. 2215 of Lecture Notes in Math. Springer, Cham (2018) 57–74. [Google Scholar]
  12. M.a.J. Cáceres, J.A. Cañizo and S. Mischler, Rate of convergence to an asymptotic profile for the self-similar fragmentation and growth-fragmentation equations. J. Math. Pures Appl. 96 (2011) 334–362. [Google Scholar]
  13. J.A. Cañizo, P. Gabriel and H. Yoldaş, Spectral gap for the growth-fragmentation equation via Harris’s theorem. Preprint arXiv:2004.08343 (2020). [Google Scholar]
  14. V. Calvez, N. Lenuzza, D. Oelz, J.-P. Deslys, P. Laurent, F. Mouthon and B. Perthame, Size distribution dependence of prion aggregates infectivity. Math. Biosci. 217 (2009) 88–99. [Google Scholar]
  15. B. Cavalli, On a family of critical growth-fragmentation semigroups and refracted Lévy processes. Acta Applicandae Mathematicae (2019). [Google Scholar]
  16. D. Chafaï, F. Malrieu and K. Paroux, On the long time behavior of the TCP window size process. Stochastic Process. Appl. 120 (2010) 1518–1534. [Google Scholar]
  17. N. Champagnat and D. Villemonais, Exponential convergence to quasi-stationary distribution and Q-process. Probab. Theory Related Fields 164 (2016) 243–283. [Google Scholar]
  18. N. Champagnat and D. Villemonais, General criteria for the study of quasi-stationarity. Working paper orpreprint (2017). [Google Scholar]
  19. B. Cloez, Limit theorems for some branching measure-valued processes. Adv. Appl. Probab. 49 (2017) 549–580. [CrossRef] [Google Scholar]
  20. M.H.A. Davis, Piecewise-deterministic Markov processes: a general class of nondiffusion stochastic models. J. Roy. Statist. Soc. Ser. B 46 (1984) 353–388. [MathSciNet] [Google Scholar]
  21. K. Deimling, Nonlinear functional analysis. Springer-Verlag, Berlin (1985). [Google Scholar]
  22. M. Doumic and M. Escobedo, Time asymptotics for a critical case in fragmentation and growth-fragmentation equations. Kinet. Relat. Models 9 (2016) 251–297. [Google Scholar]
  23. M. Doumic, M. Hoffmann, N. Krell and L. Robert, Statistical estimation of a growth-fragmentation model observed on a genealogical tree. Bernoulli 21 (2015) 1760–1799. [CrossRef] [MathSciNet] [Google Scholar]
  24. M. Doumic Jauffret and P. Gabriel, Eigenelements of a general aggregation-fragmentation model. Math. Models Methods Appl. Sci. 20 (2010) 757–783. [Google Scholar]
  25. M. Hairer, Convergence of Markov processes. Online lecturenotes (2016). [Google Scholar]
  26. N. Ikeda, M. Nagasawa and S. Watanabe, A construction of Markov processes by piecing out. Proc. Jpn. Acad. 42 (1966) 370–375. [Google Scholar]
  27. O. Kallenberg, Foundations of modern probability, Probability and its Applications (New York). Springer-Verlag, New York, second ed. (2002). [Google Scholar]
  28. P. Khashayar, B. Perthame and D. Salort, Adaptation and fatigue model for neuron networks and large time asymptotics in a nonlinear fragmentation equation. J. Math. Neurosci. (2014). [Google Scholar]
  29. I. Kontoyiannis and S.P. Meyn, Spectral theory and limit theorems for geometrically ergodic Markov processes. Ann. Appl. Probab. 13 (2003) 304–362. [CrossRef] [MathSciNet] [Google Scholar]
  30. I. Kontoyiannis and S.P. Meyn, Large deviations asymptotics and the spectral theory of multiplicatively regular Markov processes. Electr. J. Probab. 10 (2005) 61–123. [CrossRef] [MathSciNet] [Google Scholar]
  31. P. Laurençot and B. Perthame, Exponential decay for the growth-fragmentation/cell-division equation. Commun. Math. Sci. 7 (2009) 503–510. [Google Scholar]
  32. A. Marguet, A law of large numbers for branching Markov processes by the ergodicity of ancestral lineages. ESAIM: PS 23 (2019) 638–661. [EDP Sciences] [Google Scholar]
  33. A. Marguet, Uniform sampling in a structured branching population. Bernoulli 25 (2019) 2649–2695. [Google Scholar]
  34. J.A. Metz and O. Diekmann, eds., The dynamics of physiologically structured populations. Vol. 68 of Lecture Notes in Biomathematics. Papers from the colloquium held in Amsterdam, 1983. Springer-Verlag, Berlin (1986). [Google Scholar]
  35. S. Meyn and R.L. Tweedie, Markov chains and stochastic stability. With a prologue by Peter W. Glynn. Cambridge University Press, Cambridge, second ed. (2009). [Google Scholar]
  36. P. Michel, Existence of a solution to the cell division eigenproblem. Math. Models Methods Appl. Sci. 16 (2006) 1125–1153. [Google Scholar]
  37. P. Michel, S. Mischler and B. Perthame, General relative entropy inequality: an illustration on growth models. J. Math. Pures Appl. 84 (2005) 1235–1260. [CrossRef] [MathSciNet] [Google Scholar]
  38. S. Mischler and J. Scher, Spectral analysis of semigroups and growth-fragmentation equations. Ann. Inst. H. Poincaré Anal. Non Linéaire 33 (2016) 849–898. [Google Scholar]
  39. K. Pakdaman, B. Perthame and D. Salort, Relaxation and self-sustained oscillations in the time elapsed neuron network model. SIAM J. Appl. Math. 73 (2013) 1260–1279. [CrossRef] [Google Scholar]
  40. B. Perthame, Transport equations in biology. Frontiers in Mathematics, Birkhäuser Verlag, Basel (2007). [Google Scholar]
  41. B. Perthame and L. Ryzhik, Exponential decay for the fragmentation or cell-division equation. J. Differ. Equ. 210 (2005) 155–177. [Google Scholar]
  42. P.E. Protter, Stochastic integration and differential equations. Vol. 21 of Stochastic Modelling and Applied Probability. Second edition. Version 2.1, Corrected third printing. Springer-Verlag, Berlin (2005). [Google Scholar]
  43. E.J. Stewart, R. Madden, G. Paul and T. François, Aging and death in an organism that reproduces by morphologically symmetric division. PLoS Biol. 3 (2005). [Google Scholar]

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