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Research Article

Multinomial approximation to the Kolmogorov Forward Equation for jump (population) processes

ORCID Icon, ORCID Icon, ORCID Icon & ORCID Icon | (Reviewing editor)
Article: 1556192 | Received 20 Aug 2018, Accepted 02 Dec 2018, Published online: 26 Dec 2018

References

  • Aparicio, J. P., Natiello, M., & Solari, H. G. (2012). The quasi-deterministic limit of population dynamics. International Journal of Applied Mathematics and Statistics, 26(2), 30–45.
  • Durrett, R. (2001). Essentials of stochastic processes. New York: Springer Verlag.
  • Ethier, S. N., & Kurtz, T. G. (1986). Markov processes. New York: John Wiley and Sons.
  • Feller, W. (1949). On the theory of stochastic processes, with particular reference to applications (pp. 403–432). University of California Press.
  • Feller, W. (1940). On the integro-differential equations of purely discontinuous Markoff processes. Transactions of the American Mathematical Society, 480(3), 488–515. ISSN 00029947. Retrieved from http://www.jstor.org/stable/1990095
  • Fernández, M. L., Otero, M., Schweigmann, N., & Solari, H. G. (2013). A mathematically assisted reconstruction of the initial focus of the yellow fever outbreak in buenos aires (1871). Papers in Physics, 5, 50002. doi:10.4279/PIP.050002
  • Kendall, D. G. (1949). Stochastic processes and population growth. Journal of the Royal Statistical Society. Series B (Methodological), 11, 230–282. doi:10.1111/j.2517-6161.1949.tb00032.x
  • Kendall, D. G. (1950). An artificial realization of a simple “birth-and-death” process. Journal of the Royal Statistical Society. Series B (Methodological), 12, 116–119. doi:10.1111/j.2517-6161.1950.tb00048.x
  • Kolmogoroff, A. (1931). Über die analytischen methoden in der wahrscheinlichkeitsrechnung. Mathematische Annalen, 104, 415–458. ISSN 0025–5831. doi:10.1007/BF01457949
  • Malthus, T. 1798. An essay on the principle of population. www.esp.org. London: Electronic Scholarly Publishing Project. Retrieved from http://www.esp.org/books/malthus/population/malthus.pdf
  • McKendrick, A. G. (1914). Studies on the theory of continuous probabilities, with special reference to its bearing on natural phenomena of a progressive nature. Proceedings of the London Mathematical Society, s2–13, 401–416. doi:10.1112/plms/s2-13.1.401
  • Otero, M., Solari, H. G., & Schweigmann, N. (2006). A stochastic population dynamic model for Aedes aegypti: Formulation and application to a city with temperate climate. Bulletin of Mathematical Biology, 68, 1945–1974. doi:10.1007/s11538-006-9067-y
  • Solari, H. G., & Natiello, M. A. (2003). Stochastic population dynamics: The Poisson approximation. Physical Review E, 67, 31918. doi:10.1103/PhysRevE.67.031918
  • Solari, H. G., & Natiello, M. A. (2014). Linear processes in stochastic population dynamics: Theory and application to insect development. The Scientific World Journal - Journal of Probability and Statistics, 2014, ID 873624, 1–15. Retrieved from http://downloads.hindawi.com/journals/tswj/aip/873624.pdf
  • Zanotti, G., De Majo, M., Sol, I. A., Nicolás, S., Campos, R. E., & Fischer, S. (2015). New records of Aedes aegypti at the southern limit of its distribution in Buenos Aires Province, Argentina. Journal of Vector Ecology, 400(2), 408–411. doi:10.1111/jvec.12181