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Dear @Martin Hairer, thank you very much for your answer. (a) I have added an edit, which clarifies my question. (b) Could you give a more detailed explanation on your last point? Specially the part with "this is completely different".
@ChristianRemling Would you like to write down an answer on MSE? As I think that this question isn't really research level. Here is the link to the MSE question: math.stackexchange.com/questions/2338000/… Then I think one could close/delete this question in order to keep MO "clean".
This is not my own creation. If you have editor rights, feel free to correct my post. Nevertheless, could you give me a hint, how to tackle this task? Edit: I have corrected the definition of $w$.
