On a problem of adaptive estimation in Gaussian white noise. (Russian) Zbl 0725.62075
The author considers a stochastic process \(X_{\epsilon}(t)\) defined by
\[
dX_{\epsilon}(t)=S(t)dt+\epsilon d\omega (t),
\]
where \(\omega\) (t) is Gaussian white noise and \(\epsilon\to 0\). As a criterium for an appropriate estimator of \(S(t_ 0)\), \(t_ 0\) given, the author defines a special risk function. Its properties are investigated and detailed proofs are given.
Reviewer: W.Schlee (München)
MSC:
| 62M09 | Non-Markovian processes: estimation |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 62F35 | Robustness and adaptive procedures (parametric inference) |
| 62M05 | Markov processes: estimation; hidden Markov models |
| 62M99 | Inference from stochastic processes |
