Abstract
We here review in more detail the mathematical formalism underlying the modelling of stochasticity in population systems, which will be used throughout the rest of the thesis. We begin with revisiting the basic mathematical definitions which lead to the concept of homogeneous stochastic process. Those describe the dynamics of the chemical concentrations in a stochastic formalism. Homogeneous processes satisfy the master equation; the fundamental equation for the stochastic dynamics.
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References
J.D. Murray, Mathematical Biology, vol. 2 3rd edn. (Springer, Berlin, 2008)
S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. (Springer, Berlin, 2003)
C.W. Gardiner, Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences, 4th edn. (Springer, New York, 2009)
N.G. van Kampen, Stochastic Processes in Physics and Chemistry, 3rd edn. (Elsevier Science, Amsterdam, 2007)
P. Glansdorff, I. Prigogine, Thermodynamic Theory of Structure, Stability and Fluctuations (Wiley-Interscience, Chichester, 1971)
D.T. Gillespie, J. Comput. Phys. 22, 403 (1976)
D.T. Gillespie, J. Phys. Chem. 81, 2340 (1977)
A.J. McKane, T. Biancalani, T. Rogers, Bull. Math. Biol. (2013)
S. Lang, Linear Algebra (Springer, Berlin, 1987)
M.L. Mehta, Matrix Theory (Hindustan Publishing Corporation, India, 1989)
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Biancalani, T. (2014). Methods. In: The Influence of Demographic Stochasticity on Population Dynamics. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-07728-4_2
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DOI: https://doi.org/10.1007/978-3-319-07728-4_2
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