The <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$$\alpha $$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi mathvariant="italic">α</mi> </math> </EquationSource> </InlineEquation>-stable L<InlineEquation ID="IEq6"> <EquationSource Format="TEX">$$\acute{\mathrm{e}}$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mover accent="true"> <mi mathvariant="normal">e</mi> <mo>´</mo> </mover> </math> </EquationSource> </InlineEquation>vy motion together with the Poisson process and Brownian motion are the most important examples of L<InlineEquation ID="IEq7"> <EquationSource Format="TEX">$$\acute{\mathrm{e}}$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mover accent="true"> <mi mathvariant="normal">e</mi> <mo>´</mo> </mover> </math> </EquationSource> </InlineEquation>vy processes, which form the first class of stochastic processes being studied in the modern...</equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation>

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...