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Partila Differential Equations : Ito's Lemma

Please see the attached file for the fully formatted problems.
Suppose that S satisfies:

dS = a(S,t)dt + b(S,t)dX

Show that for any functions g1(S,t) and g2(S,t), the following is true:

(Note: I don't know if Itô's lemma is used in the proof or if you can use some Calculus identity or rule to determine the proof.)


Solution Summary

PDEs and Ito's lemma are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.