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Stochastic ordinary and partial differential equations generalize the concepts of ordinary and partial differential equations to the setting where the unknown is a stochastic process.

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Infinite-time, Path-Dependent Expected Value of an Orstein-Uhlenbeck process

I am dealing with an Orstein-Uhlenbeck process $X_t$ with its stochastic differential equation being $$dX_t=(\mu-X_t)dt+\sigma dW_t.$$ I want to show $$\mathbb{E}\left[\frac{|X_\infty|}{\int_{0}^{\ …