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

Abstract

It is considered Ornstein-Uhlenbeck process $x_t=x_0{e}^{-\theta t}+\mu (1-e^{-\theta t})+\sigma {\int }_0^t{e}^{-\theta (t-s)}d{W}_s$, where $x_0\in R$, $\theta >0$, $\mu \in R$ and $\sigma >0$ are parameters. By use values $(z_k{)}_{k\in N}$ of corresponding trajectories at a fixed positive moment $t$, a consistent estimate of each unknown parameter of the Ornstein-Uhlenbeck's stochastic process is constructed under assumption that all another parameters are known.

17 pages, 1 figure, 5 tables

Cited by in corpus (2)

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