 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/iii/paper-202/6/c/solution

Part a applied to the deterministic kernel gives

X_{t} \sim N (x e^{- λ t}, \int_{0}^{t} e^{- 2 λ (t - s)} d s) = N (x e^{- λ t}, \frac{1 - e ^{- 2 λ t}}{2 λ}) .

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