Statistics with diffusion crossing times. (English) Zbl 0673.62072
Probability theory and applications, Proc. World Congr. Bernoulli Soc., Tashkent/USSR 1986, Vol. 1, 131-134 (1987).
[For the entire collection see Zbl 0671.00012.]
We study a model of recurrent diffusion on \({\mathbb{R}}\), solution of: \[ dX_ t=b(\theta,X_ t)dt+\sigma dW_ t \] where W is a standard Brownian motion starting in zero. We want to estimate the unknown parameter \(\theta\) when we observe the zero crossing times of X up to the time t. We study the asymptotic properties of the estimators based on these observations when t goes to infinity.
We study a model of recurrent diffusion on \({\mathbb{R}}\), solution of: \[ dX_ t=b(\theta,X_ t)dt+\sigma dW_ t \] where W is a standard Brownian motion starting in zero. We want to estimate the unknown parameter \(\theta\) when we observe the zero crossing times of X up to the time t. We study the asymptotic properties of the estimators based on these observations when t goes to infinity.
MSC:
| 62M05 | Markov processes: estimation; hidden Markov models |
| 62F12 | Asymptotic properties of parametric estimators |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
