Nonlinear stochastic Markov processes and modeling uncertainty in populations
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 de...
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| Format: | Article |
| Language: | English |
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AIMS Press
2011-11-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2012.9.1 |
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| author | H.Thomas Banks Shuhua Hu |
| author_facet | H.Thomas Banks Shuhua Hu |
| author_sort | H.Thomas Banks |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-769c274895b541488b22b74bce82fb58 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2011-11-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-769c274895b541488b22b74bce82fb582025-01-24T02:05:22ZengAIMS PressMathematical Biosciences and Engineering1551-00182011-11-019112510.3934/mbe.2012.9.1Nonlinear stochastic Markov processes and modeling uncertainty in populationsH.Thomas Banks0Shuhua Hu1Center for Research in Scientific Computation, Center for Quantitative Sciences in Biomedicine, Raleigh, NC 27695-8212Center for Research in Scientific Computation, Center for Quantitative Sciences in Biomedicine, Raleigh, NC 27695-8212We 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.https://www.aimspress.com/article/doi/10.3934/mbe.2012.9.1forward kolmogorovuncertaintyfokker-planckprobabilistic structures on deterministic systemspointwise equivalence.nonlinear markov processes |
| spellingShingle | H.Thomas Banks Shuhua Hu Nonlinear stochastic Markov processes and modeling uncertainty in populations Mathematical Biosciences and Engineering forward kolmogorov uncertainty fokker-planck probabilistic structures on deterministic systems pointwise equivalence. nonlinear markov processes |
| title | Nonlinear stochastic Markov processes and modeling uncertainty in populations |
| title_full | Nonlinear stochastic Markov processes and modeling uncertainty in populations |
| title_fullStr | Nonlinear stochastic Markov processes and modeling uncertainty in populations |
| title_full_unstemmed | Nonlinear stochastic Markov processes and modeling uncertainty in populations |
| title_short | Nonlinear stochastic Markov processes and modeling uncertainty in populations |
| title_sort | nonlinear stochastic markov processes and modeling uncertainty in populations |
| topic | forward kolmogorov uncertainty fokker-planck probabilistic structures on deterministic systems pointwise equivalence. nonlinear markov processes |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2012.9.1 |
| work_keys_str_mv | AT hthomasbanks nonlinearstochasticmarkovprocessesandmodelinguncertaintyinpopulations AT shuhuahu nonlinearstochasticmarkovprocessesandmodelinguncertaintyinpopulations |