Discrete Recurrence

Questions
1

I’m trying to resolve Proposition 1 from the article below(page 4).

http://arxiv.org/pdf/1506.04656.pdf

Thank you.

2

Hi,

what did you try ???

There is a function RSolve which is exactly made for this kind of task:

RSolve.png
RSolve.png749×395 8.95 KB

Regards – Henrik

3

I tried in Maple because I have never used Mathematica.

I see it is better for this kind of problems.

You don’t know how much you helped me. This recurrence stressed me a lot last couple of days.

Do you think I could resolve a multivariate recurrence like Lemma1 (page 5) from the same article?

Thank you so much.

Best wishes and regards,

Raluca

4

I got this

Untitled.jpg
Untitled.jpg569×215 36.2 KB

Could you, please, tell me why?

5

Hi Raluca,

well, this is not Maple …

You need to define an equation, i.e. it should read after RSolve x[t+1] == a[t] … In a notebook both operators (= and ==) look very similar.

Regarding your question on multivariate recurrence: I may be completely wrong, but to me this seems equivalent to your first problem. In the solution there is nowhere stated that every element needs to be a scalar.

Regards – Henrik

6

Thank you Henrick. You lighted me up again.

Regarding the multivariate recurrence it can’t be the same. For example, for the bivariate recurrence t is (t1,t2).
In the same article (page 11), is a bivariate example. Do you think that it could be implemented in Mathematica, eventually in a recurrence plot?