Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Using stochastic(!) methods find explicit solution to each of the two ($i = 1, 2$) initial value problems $$\partial_t u(t, x) = \frac{1}{2} \beta^2 \partial_x^ 2 u(t, x) + (−\alpha x + \gamma )\partial_x u(t, x)$$

with $u(0, x) = f_i(x)$ where $f_1 (x) = \delta(x)$ is the Dirac function and $f_2 (x) = x$.

share|improve this question
    
What do you know about stochastic analysis? –  Jonas Teuwen Apr 24 '11 at 13:22
    
@jonas T: i studies SDE's. so, what i actually did is i took the O-U process which satisfies the Fokker-Plank equation with drift a(x-γ/β) and diffusion β^2/2, and that Xt(the OU process) is normally distributed with mean γ/β and variance β^2/2*a and then f=u(x,t). i am just worried that it is not enough and was wondering of there is another way? –  lisa Apr 24 '11 at 20:14
    
Why wouldn't that be enough? –  Jonas Teuwen Apr 24 '11 at 21:15

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.