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- #1

- Thread starter Jason
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- #1

- Feb 12, 2012

- 26

Yes, B indeed stands for a brownian motion, so you have to keep the basic properties in mind.

B0 = 0

Bt-B0 follows a normal distribution with mean 0 and variance (not standard deviation) t.

So in order to solve most of these questions, you need to know the moments of a normal distribution.

For the one involving B2*B3, you have to know that the incremets onf a brownian motion are independent. So in particular, B2*B3=(B3-B2)*B2+B2^2. So computing the expectation knowing the independence is easy.

For question f, you have to know the mgf of a normal distribution, that's all (subtract B0=0 if you have trouble seeing it).

Note for later : the advanced probability is the first thing I look for when I come at MHB, there's no need to send me a PM. If I can answer, I'll answer, if not, I'll try or I leave it

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- #3

- Feb 12, 2012

- 26

For example the first one, just note that B_0=0, so B_1 = B_1 - B_0, but the third property says that B_1-B_0 follows a normal distribution N(0,1-0), so you have to get the 4th moment of a standard normal distribution. (I think it's 3, you can get it by computing the integral or just looking on the internet).

It's always this trick, you make appear the difference between B_j and B_k and you work on it with the properties you're given. Just give it a try I really learned about brownian motion 5 months ago...

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- #5

- Feb 12, 2012

- 26

Yep, that's a good start !

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- #7

- Feb 12, 2012

- 26

Maybe you ought to put more details for the step, especially for (e).

See, not that difficult ?

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- #9