Operator Fitting for Parameter Estimation of Stochastic Differential Equations

Understand

Estimation of parameters is a crucial part of model development.

• When models are deterministic, one can minimise the fitting error; for stochastic systems one must be more careful.
• Broadly parameterisation methods for stochastic dynamical systems fit into maximum likelihood estimation- and method of moment-inspired techniques.
• We propose a method where one matches a finite dimensional approximation of the Koopman operator with the implied Koopman operator as generated by an extended dynamic mode decomposition approximation.