Brownian Motion

I could use some help with this exercise I just got.
Prove that with chance zero that limit for t->infinite (Brownian motion at time t)/(sqrt (t))=0.
I hope you understand what I mean and that you can help me.
Thanks,
Sander

Originally posted by tejo
I could use some help with this exercise I just got.
Prove that with chance zero that limit for t->infinite (Brownian motion at time t)/(sqrt (t))=0.
I hope you understand what I mean and that you can help me.
Thanks,
Sander

Are you making us do ur homework?

Originally posted by howzzat
Are you making us do ur homework?

I am not making anyone to do anything. I am just asking for help, because I still haven't solved this one.

Originally posted by tejo
I could use some help with this exercise I just got.
Prove that with chance zero that limit for t->infinite (Brownian motion at time t)/(sqrt (t))=0.
I hope you understand what I mean and that you can help me.
Thanks,
Sander

Is time discrete or continuous? Could you define Brownian motion mathematically?

Originally posted by Acolyte
Is time discrete or continuous? Could you define Brownian motion mathematically?

I hope I will explain this well.

Bt:=integral from 0 to t Ns ds.

Ns is a completely random function of t. In other words, the continuous-time analogue of a sequence of independent identically distributed random variables.
1.Ns is independent of Nt for t != (not equal) s
2.The random variables Ns (s>=0) all have the same probability distribution u
3.Expectancy of Ns = 0 (E(Nt)=0)

So Bt has the following requirements:
1.For any 0=t0<=t1<=...<=tn the random vaiables Bt(j+1) - Bt(j) are independent (j=0,...,n-1)
2.Bt has stationary increments.
3. E(Bt)=0 for all t>=0
4. E((B1)^2)=1 also true E((Bt)^2)=t
5. t->Bt is continuous a.s. with probability 1.

The Brownian Motion is also called Wiener process I believe.

Originally posted by tejo
I hope I will explain this well.

Bt:=integral from 0 to t Ns ds.

Ns is a completely random function of t. In other words, the continuous-time analogue of a sequence of independent identically distributed random variables.
1.Ns is indep ...[text shortened]... 1.

The Brownian Motion is also called Wiener process I believe.

I understand the question now. I think the following will work: Bt (for t an integer) can be turned into a discrete summation; conditions 1. and 4. imply that the summands are iid with variance 1, and then a Central Limit Theorem does the rest.

Originally posted by Acolyte
I understand the question now. I think the following will work: Bt (for t an integer) can be turned into a discrete summation; conditions 1. and 4. imply that the summands are iid with variance 1, and then a Central Limit Theorem does the rest.

Thank you very much Acolyte. It worked really well.