English

Estimation of the parameters of the Ornstein-Uhlenbeck's stochastic process

Statistics Theory 2016-08-30 v3 Statistics Theory

Abstract

It is considered Ornstein-Uhlenbeck process xt=x0eθt+μ(1eθt)+σ0teθ(ts)dWs x_t = x_0 e^{-\theta t} + \mu (1-e^{-\theta t}) + \sigma \int_0^t e^{-\theta (t-s)} dW_s, where x0Rx_0 \in R, θ>0\theta>0, μR \mu \in R and σ>0\sigma > 0 are parameters. By use values (zk)kN(z_k)_{k \in N} of corresponding trajectories at a fixed positive moment tt, a consistent estimate of each unknown parameter of the Ornstein-Uhlenbeck's stochastic process is constructed under assumption that all another parameters are known.

Keywords

Cite

@article{arxiv.1608.04507,
  title  = {Estimation of the parameters of the Ornstein-Uhlenbeck's stochastic process},
  author = {Levan Labadze and Gogi Pantsulaia},
  journal= {arXiv preprint arXiv:1608.04507},
  year   = {2016}
}

Comments

17 pages, 1 figure, 5 tables