Given a stochastic process $X_{t}$. Suppose we have the dynamic $dX_{t}=a(X_{t})dt+b(X_{t}) dW_{t}$. If I have $Y_{t}=\int_{0}^{t}X_{s} ds$, is it possible to find $dY_{t}$? What I want to express $dY_{t}=a(Y_{t})dt+b(Y_{t})dW^{1}_{t}$, I do not require that $W_{t}$ and $W_{t}^{1}$ to be the same, the can be different.
2026-04-04 17:32:37.1775323957
Finding the SDE of $\int_{0}^{t} X_{s} ds$
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