An introduction to stochastic processes with applications to biology

By Linda J. S. Allen. 2003

1,050 citations recorded by the source corpus.

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Citations in the corpus

Exactly Solvable Models of Biological Invasion (2005, background): “, see Horsthemke and Lefever (1984), Allen (2003) and references therein; for the sake of brevity we do not go into details of this approach here.”
Measurement Error in Nonlinear Models: A Modern Perspective, 2nd edition by R. J. Carroll, D. Ruppert, L. A. Stefansky, and C. M. Crainiceanu (2007, methodology): “Other key references to stochastic modeling that have been used in molecular biology and chemistry are the books by van Kampen (1992), Gillespie (1992), and Gardiner (2004). While these books are comprehensive mathematical treatments, they lack examples relevant to modern cell biology.”
A better way to estimate population trends (2009, background): “A8 can be regarded as just a recipe for simulating a trajectory of population abundance for specified values of λ and σ2 (for instance, Allen 2003, Higham 2001): (1) Over a tiny time interval dt, generate an increment dX(t) of log-abundance from a normal distribution with a mean of (ln λ)dt and a…”
Environmental variability and mean-reverting processes (2016, background): “, [3, 4, 5, 6, 8, 10, 18, 21, 23]), it is assumed that changes in the environment produce random changes in a population’s per capita birth and death rates that are independent from the changes due to demographic variability.”
Relativistic Brownian Motion (2008, background): “3 Nowadays, the modern theory of stochastic processes goes far beyond the original problem considered by Einstein and his contemporaries, and the applications cover a wide range of different areas, including physics [77–84], biology [85,86], economy and finance [87–89].”
The power of a good idea: Quantitative modeling of the spread of ideas from epidemiological models (2005, methodology): “Dynamical population models are used to predict average behavior, generate hypotheses or explore mechanisms across many fields of science including ecology [1–3], epidemiology [4–7] and immunology [8], to name but a few.”
Stochastic Models for Structured Populations: Scaling Limits and Long Time Behavior (2015, background): “Some of the following computation can be found in [51] or in [2], but they are finely developed in [9].”
WKB theory of large deviations in stochastic populations (2016, background): “Chaos 18 1727 [19] Landau L D and Lifshitz E M 1991 Quantum Mechanics (Oxford: Pergamon) [20] Freidlin M I and Wentzell A D 1984 Random Perturbations of Dynamical Systems (New York: Springer-Verlag) [21] Dykman M I and Krivoglaz M A 1984, in Soviet Physics Reviews ed I M Khalatnikov (New York: Harwo”
Reproduction numbers of infectious disease models (2017, background): “There are many discrete time epidemic models in the literature; see, for example, Allen (1994) and Yakubu (2010).”
Stochastic persistence and stationary distribution in a Holling–Tanner type prey–predator model (2012, background): “The available stochastic formalisms can be divided into two broad classes, one of them is known as discrete or continuous time Markov Chain modeling (see [45–50]) and other is the noise added systems [28, 51–65].”
Construction of Equivalent Stochastic Differential Equation Models (2008, methodology): “Also, for the first procedure, similarities are straightforward to obtain between the forward Kolmogorov differential equations satisfied by the probability distributions of the discreteand continuous-time stochastic models and these similarities alow one to infer an Itô SDE model from the discrete ”
Allee Effects, Propagule Pressure and the Probability of Establishment: Risk Analysis for Biological Invasions (2006, background): “Stochastic differential equation (SDE) representations of population growth are stochastic generalizations of the familiar deterministic models of population growth (ordinary differential equations – ODEs) obtained by the addition of a term for random perturbations (Allen 2003).”