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August  2013, 18(6): 1611-1631. doi: 10.3934/dcdsb.2013.18.1611

## Parameter estimation by quasilinearization in differential equations with state-dependent delays

 1 Department of Mathematics and Computing, University of Pannonia, H-8201 Veszprém, P.O.Box 158

Received  January 2012 Revised  February 2012 Published  March 2013

In this paper we study a parameter estimation method in functional differential equations with state-dependent delays using a quasilinearization technique. We define the method, prove its convergence under certain conditions, and test its applicability in numerical examples. We estimate infinite dimensional parameters such as coefficient functions, delay functions and initial functions in state-dependent delay equations. The method uses the derivative of the solution with respect to the parameters. The proof of the convergence is based on the Lipschitz continuity of the derivative with respect to the parameters.
Citation: Ferenc Hartung. Parameter estimation by quasilinearization in differential equations with state-dependent delays. Discrete & Continuous Dynamical Systems - B, 2013, 18 (6) : 1611-1631. doi: 10.3934/dcdsb.2013.18.1611
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