Basic Stochastic DE

• Mar 9th 2008, 12:44 PM
paolopiace
Basic Stochastic DE
Hello!

I really hope someone can show to me how to resolve the following stochastic differential equation, where W(t) is the Wiener process:

$
dY(t) = Y(t) dW(t)\
$

with Y(0) = 1

Result is: exp[W(t) - (t/2)]

Thanks in any case!
• Mar 14th 2008, 04:50 AM
mr fantastic
Quote:

Originally Posted by paolopiace
Hello!

I really hope someone can show to me how to resolve the following stochastic differential equation, where W(t) is the Wiener process:

$
dY(t) = Y(t) dW(t)\
$

with Y(0) = 1

Result is: exp[W(t) - (t/2)]

Thanks in any case!