vassilis

Posted on Thursday, 04 December, 2003 - 05:09 pm:

Hello, can you help me?

I have the following equation and I have to find what is the Lim when $t \to \infty$

$V (Z_{t}) = ((ls)^{2}) / n \times (1 - (1 - λ {))}^{2 t} / (1 - (1 - λ {))}^{2}$

David Loeffler

Posted on Thursday, 04 December, 2003 - 06:32 pm:

λ

fixed (independent of time)? If so, how big is it? It might help you to observe that

1 - (1 - λ) = λ

David

vassilis

Posted on Thursday, 04 December, 2003 - 07:02 pm:

I made some mistakes in the equation:
the first l (ls) is also lambda and also the power 2t and 2 are only for (1-lambda), and not for (1-(1-lambda).I put the brackets incorrectly.
sorry about that.

lambda takes values between (0,1].

David Loeffler

Posted on Thursday, 04 December, 2003 - 11:20 pm:

So is your function
LaTeX Image

David

vassilis

Posted on Friday, 05 December, 2003 - 12:20 pm:

the top part is

(λ s)^{2} (1 - (1 - λ)^{2 t})

the other part is: $n (1 - (1 - λ)^{2})$

David Loeffler

Posted on Friday, 05 December, 2003 - 02:22 pm:

Ah. I see. Well, you can safely ignore anything that doesn't depend on t. Now LaTeX Image

, so

.
Hence your expression as a whole tends to
LaTeX Image

David

vassilis

Posted on Friday, 05 December, 2003 - 05:16 pm:

Thanks for the reply. It just clicked when you pointed that out!