Infinite-sample consistent estimations of parameters of the Wiener process with drift

Abstract

We consider the Wiener process with drift $$d{X}_t=\mu dt+\sigma d{W}_t$$ with initial value problem $X_0=x_0$, where $x_0\in R$, $\mu \in R$ and $\sigma >0$ are parameters. By use values $(z_k{)}_{k\in N}$ of corresponding trajectories at a fixed positive moment $t$, the infinite-sample consistent estimates of each unknown parameter of the Wiener process with drift are constructed under assumption that all another parameters are known. Further, we propose a certain approach for estimation of unknown parameters $x_0,\mu ,\sigma$ of the Wiener process with drift by use the values $(z_k^{(1)}{)}_{k\in N}$ and $(z_k^{(2)}{)}_{k\in N}$ being the results of observations on the $2k$-th and $2k+1$-th trajectories of the Wiener process with drift at moments $t_1$ and $t_2$ , respectively.

12 pages, 1 figures, 4 tables. arXiv admin note: substantial text overlap with arXiv:1608.04507

References in corpus (1)

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

Cited by in corpus (1)

• On a consistent estimator of a useful signal in Ornstein-Uhlenbeck model in $\mathbb{C}[-l,l[$