Question: 3.10. Consider the PDE u t + u x+ 12 2u x2 =0 . One solution is u(t,x) = x22xt+t2t. Write down the corresponding SDE,

3.10. Consider the PDE ∂u

∂t + ∂u

∂x+ 12

∂2u

∂x2 =0 . One solution is u(t,x) = x2−2xt+t2−t.

Write down the corresponding SDE, and its solution X(t), and then verify the Feynman–Kac formula for solutions with initial condition X(s) = y .

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