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I have a question about the use of Dynkin's formula. Suppose I have a stochastic process $X_t$, from an SDE that I cannot solve analytically. I want to find the expectation $\mathbb{E}X_t$. By Dynkin with initial condition $X_0=x$,

$$\mathbb{E}X_t=x+\mathbb{E}^x\int_0^t L(X_s)ds$$

,here $L$ is the generator of the diffusion, found from the SDE. How would one find an expression for the expectation of the integral?

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