Parameter Estimation for Random Di erential Equation Models

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Parameter Estimation for Random Differential Equation Banks and Michele L. JoynerCenter for Research in Scientific ComputationNorth Carolina State UniversityRaleigh, NC, United StatesandDept of Mathematics and StatisticsEast Tennessee State UniversityJohnson City, TN 37614December 13, 2016AbstractWe consider two distinct techniques for estimating Random parameters in Random differential Equation (RDE) Models . In one approach, the solution to a RDE is represented by a collection of solution trajectories inthe form of sample deterministic equations . In a second approach we employ pointwise equivalent stochasticdifferential Equation (SDE) representations for certain RDEs. Each of the approaches is tested using deter-ministic model comparison techniques for a logistic growth model which is viewed as a special case of a moregeneral Bernoulli growth model. We demonstrate efficacy of the preferred method with experimental datausing algae growth model words: Parameter Estimation , Random differential equations , stochastic differential Equation equiv-alents, model comparison techniquesMathematics Subject Classification: 34K29, 34K50, 65L09, 37H10, 49N4511 IntroductionIn this paper, we examine techniques for estimating Random variable parameters in Random differentialequation (RDE) Models .

less advanced than that for stochastic di erential equations (SDE). While the questions of existence and uniqueness of solutions are without question important, for this presentation we simply assume that the RDE we investigate have a unique solution, and focus on …

  Equations, Stochastic, Erential, Di erential, Stochastic di erential equations