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Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.
1
vote
Integral over a point process. Asymptotic of the dispersion
Sorry, I don't have the answer. But, this belongs to the generalized shot noise studied by John Rice. This might help:
John Rice. On Generalized Shot Noise. Advances in Applied Probability. Vol. 9, …
2
votes
2
answers
1k
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Gaussian expectation of an exponentiated outer product
Given a normal random column vector $\mathbf{x} \sim N(\mu, \Sigma)$, I need the expectation,
$$ E\left[ \exp(\mathbf{xx}^\top)\right]$$
where $\exp(\cdot)$ is element-wise exponential function (not …