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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.

10 votes
1 answer
210 views

Distribution of the maximum of the norm of k-averages of n i.i.d. d-dimensional random vectors

Suppose $X_1, ... X_n$ are i.i.d. random vectors in $d$-dimensional space (i.e., $R^d$) with continuous centrally symmetric density function $f(\cdot)$ (i.e., symmetric with respect to the origin). Fo …
Marcos Kiwi's user avatar
2 votes
0 answers
70 views

Inequalities concerning cummulative distributions of binomials

For random variable $Z$, let $F_Z$ denote its cdf, i.e., $F_Z(t)=\mathbb{P}(Z\leq t)$. Let $X$ be a binomial distribution with parameters $(n,p)$ and $Y$ a binomial distribution with parameters $(m,p) …
Marcos Kiwi's user avatar