Question: Please help to solve this Stochastic Calculus question. Detailed steps are required. Many thanks! Exercise 6.35. (i) Derive a general formula for the solution to

Please help to solve this Stochastic Calculus question. Detailed steps are required. Many thanks!

Exercise 6.35. (i) Derive a general formula for the solution to the following linear SDE: dXt = (AXt + a(t) ) dt + o(t)dBt. Here A is a deterministic n x n matrix, the coefficients a(t), o(t) are bounded, deterministic functions taking values in Mat(n, 1) and Mat(n, d) respectively, and B is a d-dimensional Brownian motion. (ii) Use the formula obtained in Part (i) to solve the equation of stochastic har- monic oscillator: dXt = Ydt, mdYt = -kXtdt - cYtdt + odBt. where m, k, c, o are given positive constants and B is a one-dimensional Brownian motion

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