Abstract
We study the first-passage times for models of individual growth of animals in randomly fluctuating environments. In particular, we present results on the mean and variance of the first-passage time by a high threshold value (higher than the initial size). The models considered are stochastic differential equations of the form \(dY (t) =\beta \left (\alpha -Y (t)\right )dt +\sigma dW(t),\) Y (t 0) = y 0, where Y (t) = g(X(t)) is a transformed size, g being a strictly increasing C 1 function of the actual animal size X(t) at time t, σ measures the effect of random environmental fluctuations on growth, W(t) is the standard Wiener process, and y 0 is the transformed size (assumed known) at the initial instant t 0. Results are illustrated using cattle weight data, to which we have applied the Bertalanffy-Richards (g(x) = x c) and the Gompertz (g(x) = lnx) stochastic models.
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Acknowledgements
The authors are members of the Centro de Investigação em Matemática e Aplicações, the research center of the Universidade de Évora financed by FCT (Fundação para a Ciência e Tecnologia). This work was partially financed by FCT within the research project PTDC/MAT/64297/2006.
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Carlos, C., Braumann, C.A., Filipe, P.A. (2013). Models of Individual Growth in a Random Environment: Study and Application of First Passage Times. In: Lita da Silva, J., Caeiro, F., Natário, I., Braumann, C. (eds) Advances in Regression, Survival Analysis, Extreme Values, Markov Processes and Other Statistical Applications. Studies in Theoretical and Applied Statistics(). Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34904-1_10
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DOI: https://doi.org/10.1007/978-3-642-34904-1_10
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