Estimation in Interacting Diffusions: Continuous and Discrete Sampling

Jaya Prakash Narayan Bishwal

doi:10.4236/am.2011.29160

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Estimation in Interacting Diffusions: Continuous and Discrete Sampling

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DOI: 10.4236/am.2011.29160 5,043 Downloads 7,746 Views Citations

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Jaya Prakash Narayan Bishwal

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ABSTRACT

Consistency and asymptotic normality of the sieve estimator and an approximate maximum likelihood estimator of the drift coefficient of an interacting particles of diffusions are studied. For the sieve estimator, observations are taken on a fixed time interval [0,T] and asymptotics are studied as the number of interacting particles increases with the dimension of the sieve. For the approximate maximum likelihood estimator, discrete observations are taken in a time interval [0,T] and asymptotics are studied as the number of interacting particles increases with the number of observation time points.

KEYWORDS

Stochastic Differential Equations, Mean-Field Model, Large Interacting Systems, Diffusion Process, Discrete Observations, Approximate Maximum Likelihood Estimation, Sieve Estimation

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

J. Bishwal, "Estimation in Interacting Diffusions: Continuous and Discrete Sampling," Applied Mathematics, Vol. 2 No. 9, 2011, pp. 1154-1158. doi: 10.4236/am.2011.29160.

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