Recursive identification in continuous-time stochastic processes

David Levanony, Adam Shwartz, Ofer Zeitouni

Research output: Contribution to journalArticlepeer-review

17 Scopus citations

Abstract

Recursive parameter estimation in diffusion processes is considered. First, stability and asymptotic properties of the global, off-line MLE (maximum likelihood estimator) are obtained under explicit conditions. The MLE evolution equation is then derived by employing a generalized Itô differentiation rule. This equation, which is highly sensitive to initial conditions, is then modified to yield an algorithm (infinite dimensional in general) which results in an estimator that, irrespective of initial conditions, is consistent and asymptotically efficient and in addition, converges rapidly to the MLE. The structure of the algorithm indicates that well known gradient and Newton type algorithms are first-order approximations. The results cover a wide class of processes, including nonstationary or even divergent ones.

Original languageEnglish
Pages (from-to)245-275
Number of pages31
JournalStochastic Processes and their Applications
Volume49
Issue number2
DOIs
StatePublished - 1 Jan 1994
Externally publishedYes

Keywords

  • continuous time algorithms
  • diffusion processes
  • evolution equations
  • maximum likelihood
  • parameter estimation

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