# American Institute of Mathematical Sciences

2012, 9(1): 1-25. doi: 10.3934/mbe.2012.9.1

## 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, United States, United States

Received  January 2011 Revised  July 2011 Published  December 2011

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. Mathematical Biosciences & Engineering, 2012, 9 (1) : 1-25. doi: 10.3934/mbe.2012.9.1
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##### References:
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