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Hello !

Is it theoretically possible that a certain type of generator could provide a limited current of 10 mA at a voltage of 1000 V in a load of 2000 ohms without any noticeable change in intensity and voltage mentioned previously?

yes, but with a regulation, not easy to achieve.

http://fr.wikipedia.org/wiki/Loi_d%27Ohm

Thank you for the answer,

That is, the generator would have an internal resistance of 100 000 ohms? If we add a load of 2000 ohms at the output, the current would be 9,8 mA (unless the internal resistance drops to 98 000 ohms to maintain a current of 10 mA?) Is the principle of the regulated current? do not know too much ...)

What is not easy to achieve?
(Maybe without regulation, it's probably easier to do?)

But with such an internal resistance, the output voltage will not drop and remain at 1000 V? (Ohm's law keeps some mysteries to me).

You will not have 1000V at the load terminals of 2000 Ohms, but at the terminals of the set (load + generator output resistance).
10mA on 2000 Ohms will never do more than 20V.