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In probability and statistics, a probability distribution assigns a probability to each measurable subset of the possible outcomes of a random experiment, survey, or procedure of statistical inference.

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Tail of solutions of a stochastic differential equation

You want to consider: $$dx_t=f(x_t)dt + \sigma(x_t)dW_t$$ In dimension 1, you can express analytically the stationary probability density (if it exists) as: $$P(x)=\frac{1}{Z}\exp(-\int^x \frac{f(u …
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