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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.

3 votes
3 answers
2k views

Probability of a given string being a substring of another string

I am in interested into the following problem. We are given an alphabet $\Sigma$ of $k$ letters and a fixed string $S_1$ of length $l$ defined over $\Sigma$. Given a probability distribution $D$ over …
0 votes
1 answer
254 views

Entropy of a refinement of a partition

We consider a probability space $(X, B, \mu)$. Let $\alpha$ and $\beta$ be countable partitions of X. We suppose $\beta$ is a refinement of $\alpha$, ie that every set in $\alpha$ is a union of sets i …