Ricerche di Matematica

, Volume 58, Issue 1, pp 103–127 | Cite as

On the asymptotic behavior of the parameter estimators for some diffusion processes: application to neuronal models

  • Maria Teresa Giraudo
  • Rosa Maria Mininni
  • Laura Sacerdote


We consider a sample \({\left\{T_n\right\}_{1\leq n\leq N}}\) of i.i.d. times and we interpret each item as the first-passage time (FPT) of a diffusion process through a constant boundary. The problem is to estimate the parameters characterizing the underlying diffusion process through the experimentally observable FPT’s. Recently in Ditlevsen and Lánský (Phys Rev E 71, 2005) and Ditlevsen and Lánský (Phys Rev E 73, 2006) closed form estimators have been proposed for neurobiological applications. Here we study the asymptotic properties (consistency and asymptotic normality) of the class of moment type estimators for parameters of diffusion processes like those in Ditlevsen and Lánský (Phys Rev E 71, 2005) and Ditlevsen and Lánský (Phys Rev E 73, 2006). Furthermore, to make our results useful for application instances we establish upper bounds for the rate of convergence of the empirical distribution of each estimator to the normal density. Applications are also considered by means of simulated experiments in a neurobiological context.


Diffusion processes First-passage time Moment type estimators Asymptotic properties Rate of convergence Neuronal models 

Mathematics Subject Classification (2000)

62M05 62F12 60J60 62P10 


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Copyright information

© Università degli Studi di Napoli "Federico II" 2009

Authors and Affiliations

  • Maria Teresa Giraudo
    • 1
  • Rosa Maria Mininni
    • 2
  • Laura Sacerdote
    • 1
  1. 1.Department of MathematicsUniversity of TorinoTorinoItaly
  2. 2.Department of MathematicsUniversity of BariBariItaly

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