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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 views

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_ …
Raphaël Kalfon's user avatar
2 votes
0 answers
97 views

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, . …
Raphaël Kalfon's user avatar