Help for the stochastic differential equations

[ptc_scr]

Hi,

Could some one help me to solve the equations ?
dX =sqrt(X) dB

where X is a process; B is a Brownian motion with B(0,w) =0;sqrt(X) is squart root of X.

 

[chiro]

Hi,

Could some one help me to solve the equations ?
dX =sqrt(X) dB

where X is a process; B is a Brownian motion with B(0,w) =0;sqrt(X) is squart root of X.

Hey ptc_scr and welcome to the forums.

In these forums, we require the poster to show any work that they have done before we can help them. We do this so that you can actually learn for yourself what is going on so that you do the work and end up understanding it yourself.

So first I ask you to show any working, and secondly what do you know about solving SDE's with Brownian motion? Do you know about Ito's lemma and its assumptions?

 

[ptc_scr]

Hi,

I just try to assign Y=sqrt(X) and use Ito lemma to solve the problem. so
dY= 1/2 dB+ 1/(4Y) dt.

Obviously, we cannot put Y one left side. So the substitution is failed.
ANy one can show me how to find a good substitution or show me it is impossible to solve the problem ?
But for existence and uniqueness theorm for Ito-diffusion, it seems that the problem can be solve ?
because sqrt(X) <= C(1+|X|) for some certain C.

Thanks