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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.
2
votes
1
answer
105
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Estimation of the expected number of sites visited by i.i.d
Let $X_1,X_2,...$ be i.i.d variables with value in $\mathbb{N}$ (not necessarily finitely supported). Suppose $E(X_1) < \infty$.
Denote :
$$R_n = \textbf{Card}\{X_1,...,X_n\}$$
I must prove that $E(R_ …
2
votes
0
answers
97
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A characterization of Shannon entropy in finite sets?
I am trying to solve a complicated probability problem related to Shannon Entropy.
Let $(E,p)$ be a finite set with a probability measure $p$ on $E$. $E^n$ is given the probability measure $p^n(x_1, . …