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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?2011-04-24
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    @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?2011-04-24
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    Why wouldn't that be enough?2011-04-24

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