We consider adaptive Bayesian estimation of both drift and diffusion coefficient parameters for ergodic multidimensional diffusion processes based on sampled data. Under a general condition on the discretization step of the sampled data, three kinds of adaptive Bayes type estimators are proposed...

By means of the Malliavin Calculus, we derive asymptotic expansion of the probability distributions of statistics for systems perturbed by small noises. These results are applied to the problem of the second order asymptotic efficiency of the maximum likelihood estimator.

In a class of continuous-time filtering models with Gaussian limit, we provide a practical scheme of an approximation of a conditional expectation given finite-dimensional observations, in the light of the double Edgeworth expansion. Simple and explicit expressions up to the second order are...

By means of the Malliavin calculus, we present an expansion formula for the distribution of a random variableFhaving a stochastic expansionF=F0+R, whereF0is an easily tractable random variable andRis the remainder term. From this result, we derive an expansion of the distribution of the scale...

The maximum likelihood estimation of the unknown parameter of a diffusion process based on an approximate likelihood given by the discrete observation is treated when the diffusion coefficients are unknown and the condition for "rapidly increasing experimental design" is broken. The asymptotic...

An asymptotic distribution theory of the nonsynchronous covariation process for continuous semimartingales is presented. Two continuous semimartingales are sampled at stopping times in a nonsynchronous manner. Those sampling times possibly depend on the history of the stochastic processes and...