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Results tagged with pr.probability
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user 61785
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
Is a tight finite measure necessarily separately-valued and uniquely determined by its chara...
I decided not to "comment-answer" this question, so other people have duplicated some of my answer in the comments.
Since there are several questions, I will separate them and answer them individually …
- 3,768
15
votes
Accepted
Is defining measures as functionals ever insufficiently general in practice?
The first time I taught myself rigorous measure theory, I used the "linear functionals on $C(X)$" approach for compact Hausdorff spaces, so I got first-hand knowledge of where it doesn't work for prob …
- 3,768
2
votes
Properties of measures that are not countably additive but have countably additive null ideals
$\newcommand{\N}{\mathbb{N}}\newcommand{\R}{\mathbb{R}}$There are examples on $\R$ with the Borel $\sigma$-algebra $\mathcal{B}$. We take the null ideal to be the meagre Borel sets $\mathcal{M}$ (the …
- 3,768
4
votes
Is the separability of the space needed in the proof of the Prohorov's theorem?
Separability is not necessary. In fact, tightness of a family of Borel probability measures implies relative compactness in the vague/weak-* topology on any completely regular space. For instance, thi …
- 3,768