A problem of goodness-of-fit test for ergodic diffusion processes is presented. In the null hypothesis the drift of the diffusion is supposed to be in a parametric form with unknown shift parameter. Two Cramer–von Mises type test statistics are studied. The first test uses the local time...

A test procedure to detect a change in the value of the parameter in the drift of a diffusion process is proposed. The test statistic is asymptotically distribution free under the null hypothesis that the true parameter does not change. Also, the test is shown to be consistent under the...

The problem of nonparametric invariant density function estimation of an ergodic diffusion process is considered. The local asymptotic minimax lower bound on the risk of all the estimators is established. The asymptotic risk considered measures the distance between the estimators and the density...