# Stochastic differential equation

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 $f_2 (x) = x$.

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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