Jul 15, 2023 · This also explains why probability seems to have "its own words" (random variable, expected value, etc) for measure theory concepts (measurable function, integral, etc): probability had …

what are some good books on probabilities and measure theory? I already know basic probabalities, but I'm interested in sigma-algrebas, filtrations, stopping times etc, with possibly examples of "...

May 1, 2011 · 6 Noel Vaillant's online Probability Tutorials are an excellent introduction to the real analysis, general topology and measure theory foundations of probability theory.

Oct 8, 2015 · A stochastic process is a colection of random variables defined on the same probability space. Please explain further what parts of this definition are escaping you.

Jan 13, 2011 · An introductory course on probability theory can either dwell on discrete probability or continuous probability. Discrete probability, which deals with discrete events (e.g. the probability that …

For questions solely about the modern theoretical footing for probability, for example, probability spaces, random variables, law of large numbers, and central limit theorems. Use [tag:probability] instead for …

Aug 6, 2023 · How exactly did the relationship between Measure Theory and Probability Theory revolutionize Probability Theory? If I understand things correctly, it seems like the field of Probability …

Probability theory supplements that with the multiplication rule which describes independence; and things are already looking up. But what really enriches and enlivens things is that we deal with lots of …

Dec 20, 2020 · It's probably worth your looking at Billingsley's Probability and Measure, the third edition of which is widely regarded as a classic in the field. I haven't looked at it myself, but two other books …

Apr 9, 2011 · 65 For probability theory as probability theory (rather than normed measure theory ala Kolmogorov) I'm quite partial to Jaynes's Probability Theory: The Logic of Science. It's fantastic at …