Re: brownian motion
- From: David C. Ullrich <ullrich@xxxxxxxxxxxxxxxx>
- Date: Tue, 16 May 2006 09:45:28 -0500
On Tue, 16 May 2006 09:24:32 -0500, David C. Ullrich
<ullrich@xxxxxxxxxxxxxxxx> wrote:
On 16 May 2006 04:51:48 -0700, "Fedor" <malabar_carotte@xxxxxxxxx>
wrote:
oh, sorry for my bad english. I mean that I'm looking for the law of
time when the brownian motion will touch the unit sphere, that is the
T(w)=inf(t such that |B_t(w)|=1).
Your English had nothing to do with it, I just did't
read the question carefully enough, sorry.
Seems like it should be easy to at least write down
the answer as a certain integral; whether one can
evaluate that integral in closed form is not so
clear, I suspect it may depend on whether n is
even or odd.
I started writing down formulas, but I had to leave out
all the constants, so never mind the formulas. We know
what the law of B_t is. That means that we know what
P(|B_t| > 1} is for any given t. But
P(T < t) = P(|B_t| > 1),
simply because T < t and |B_t| > 1 are actually
the same event.
Aargh. That seemed much too simple, and indeed it is;
my first guess, that I had no idea what the answer
was, was correct.
What's above would be correct if B_t never returned
to the ball after leaving it. Sorry again.
************************
David C. Ullrich
.
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