Please answer the question below:

Problem 3. Feynman-Kac application We consider the stochastic process (X?)so given by X, = e", where (Wt) is a Brownian motion. Part A. (a) Determine the stochastic differential equation satisfied by the process (X.). (b) We want to determine g(t, X.) = E[X,|]. Use Feynman-Kac formula and the result of (a) to write the PDE (with its terminal condition) that the function g has to solve. (c) We guess that g has to be a polynomial of degree 2 in 2. Determine g by solving the PDE. (d) We can directly calculate the result using properties of conditional expectation. Verify that you obtain the same solution