An Inverse Problem for a Class of Conditional Probability Measure-Dependent Evolution Equations.

ABSTRACT: We investigate the inverse problem of identifying a conditional probability measure in measure-dependent evolution equations arising in size-structured population modeling. We formulate the inverse problem as a least squares problem for the probability measure estimation. Using the Prohorov metric framework, we prove existence and consistency of the least squares estimates and outline a discretization scheme for approximating a conditional probability measure. For this scheme, we prove general method stability. The work is motivated by Partial Differential Equation (PDE) models of flocculation for which the shape of the post-fragmentation conditional probability measure greatly impacts the solution dynamics. To illustrate our methodology, we apply the theory to a particular PDE model that

SUBMITTER: Mirzaev I 

PROVIDER: S-EPMC5352987 | biostudies-literature | 2016

REPOSITORIES: biostudies-literature