stochastic processes- Brownian motion

$Go Back$		Math Help Forum > University Math Help > Advanced Applied Math
$Reload this Page$ stochastic processes- Brownian motion

$Reply$

Thread Tools

Display Modes

$Old$ September 22nd, 2009, 01:22 AM

$elenaas's Avatar$

elenaas $elenaas is offline$

Junior Member

Join Date: Sep 2009

Posts: 26

Country:

Thanks: 1

Thanked 0 Times in 0 Posts

$elenaas is on a distinguished road$

$Default$ stochastic processes- Brownian motion

let $B_{t}$ be Brownian motion on R, $B_{0} = 0$ .
a) Prove that
$E\left [ exp(iuB_{t}) \right ] = exp( - \frac {1}{2}u^{2}t)$ for all $u\epsilon R$
b) Use power series expansion of the exponential function on both sides, compare the terms with the same power of u and deduse that
$E\left [ B_{t}^{4} \right ] = 3t^{2}$
c) Prove that
$E\left [ f(B_{t}) \right ] = \frac {1}{\sqrt {2\pi t}}\int f\left ( x \right )e^{ - \frac {x^{2}}{2t}}dx$
for all functions f such that the integral of the right converges.

$Reply With Quote$

$Reply$

« stochastic processes | Top | Solving Linear Equations »

Thread Tools
$Show Printable Version$ Show Printable Version $Email this Page$ Email this Page
Display Modes
$Linear Mode$ Linear Mode $Hybrid Mode$ Switch to Hybrid Mode $Threaded Mode$ Switch to Threaded Mode

Posting Rules
You may not post new threads You may not post replies You may not post attachments You may not edit your posts BB code is On Smilies are On [IMG] code is On HTML code is Off Trackbacks are Off Pingbacks are Off Refbacks are Off

Forum Jump

All times are GMT -7. The time now is 12:02 AM.

Math Help Forum is a community of maths forums with an emphasis on maths help in all levels of mathematics.
Register to post your math questions or just hang out and try some of our math games or visit the arcade.