Nonlinear Stochastic Markov Processes and Modeling Uncertainty in Populations
NORTH CAROLINA STATE UNIV AT RALEIGH CENTER FOR RESEARCH IN SCIENTIFIC COMPUTATION
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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 probabilis- tic 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.
- Statistics and Probability