Exercise 13.12 Consider the linear SDE where (t), (t), (t), and (t) are deterministic functions of time

Exercise 13.12 Consider the linear SDE

where α(t), β(t), γ(t), and δ(t) are deterministic functions of time t. Suppose that X(t) = U(t)V (t), where U(0) = 1, V (0) = X(0) and

for some a(t) and b(t). Determine U(t) and V (t) and show that the solution to the SDE is given by

Confirm that the solution to the SDE (13.40) is given by (13.41).

Transcribed Image Text:

dX = (a(t)+B(t)X)dt + (y(t) + 8(t)X)dz, 0