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Mathematical Biosciences and Engineering

2012, Volume 9, Issue 1: 1-25. doi: 10.3934/mbe.2012.9.1
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Nonlinear stochastic Markov processes and modeling uncertainty in populations

  • 1.
    Center for Research in Scientific Computation, Center for Quantitative Sciences in Biomedicine, Raleigh, NC 27695-8212
  • Received: 01 January 2011 Accepted: 29 June 2018 Published: 01 December 2011

  • MSC : 60J60, 60J22, 35Q84.

  • We consider an alternative approach to the use of nonlinear stochastic Markov processes (which have a Fokker-Planck or Forward Kolmogorov representation for density) in modeling uncertainty in populations. These alternate formulations, which involve imposing probabilistic structures on a family of deterministic dynamical systems, are shown to yield pointwise equivalent population densities. Moreover, these alternate formulations lead to fast efficient calculations in inverse problems as well as in forward simulations. Here we derive a class of stochastic formulations for which such an alternate representation is readily found.

    Citation: H.Thomas Banks, Shuhua Hu. Nonlinear stochastic Markov processes and modeling uncertainty in populations[J]. Mathematical Biosciences and Engineering, 2012, 9(1): 1-25. doi: 10.3934/mbe.2012.9.1

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  • We consider an alternative approach to the use of nonlinear stochastic Markov processes (which have a Fokker-Planck or Forward Kolmogorov representation for density) in modeling uncertainty in populations. These alternate formulations, which involve imposing probabilistic structures on a family of deterministic dynamical systems, are shown to yield pointwise equivalent population densities. Moreover, these alternate formulations lead to fast efficient calculations in inverse problems as well as in forward simulations. Here we derive a class of stochastic formulations for which such an alternate representation is readily found.


  • This article has been cited by:

    1. H.T. Banks, S. Hu, Propagation of Growth Uncertainty in a Physiologically Structured Population, 2012, 7, 0973-5348, 7, 10.1051/mmnp/20127503
    2. 2012, 978-1-4398-8083-8, 241, 10.1201/b12209-19
    3. Juan C. Cortés, Sandra E. Delgadillo-Alemán, Roberto A. Kú-Carrillo, Rafael J. Villanueva, Probabilistic analysis of a class of impulsive linear random differential equations forced by stochastic processes admitting Karhunen-Loève expansions, 2022, 15, 1937-1632, 3131, 10.3934/dcdss.2022079
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