Recently the International mathematical community celebrated the 70th anniversary of our distinguished colleague and friend Prof. Ole E. Barndorff-Nielsen. In March 20-24, 2006 the Centro de Investigación en Matemáticas (CIMAT) in Guanajuato, Mexico was host of the big International Conference on Stochastics in Science in Honor of Ole E. Barndorff-Nielsen. I was invited by the Organizing Committee to deliver a talk in a field where Ole worked and is working, as usual very efficient, now. Taking it into account, I decided that the right theme from Ole's interests should be Turbulence. As a result of this idea I have proposed the talk On the classical, statistical, and stochastic approaches to the hydrodynamic turbulence, slides of which is presented in this booklet. So, this talk is for Ole to whom I have great respect and love.