Nonlinear Stochastic Markov Processes and Modeling Uncertainty in Populations

Abstract

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.

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Document Details

Document Type
Technical Report
Publication Date
Jul 06, 2011
Accession Number
ADA556799

Entities

People

  • H. Thomas Banks
  • Shuhua Hu

Organizations

  • North Carolina State University

Tags

Communities of Interest

  • Biomedical

DTIC Thesaurus Topics

  • Differential Equations
  • Equations
  • Fokker Planck Equations
  • Gaussian Processes
  • Inverse Problems
  • Kolmogorov Equations
  • Markov Processes
  • Mathematics
  • Nonlinear Differential Equations
  • Normal Distribution
  • Probability
  • Probability Density Functions
  • Probability Distributions
  • Random Variables
  • Stochastic Processes
  • Uncertainty

Fields of Study

  • Mathematics

Readers

  • Computational Modeling and Simulation
  • Mathematical Modeling and Probability Theory.