probability

If real random variables X, Y (with cdf's FX and FY) are each defined on a probability space (𝛀,ℬ,P), they are defined to be independent precisely when their joint cumulative distribution F(s,t) = ...

Answer by James Baxter for Reference request: book on stochastic calculus (not finance)

When I say "Advanced Probability", I mean for a person acquainted with the measure-theoretic foundations of probability theory, that wants to learn about Stochastic Processes from there, in discrete and continuous time (including martingales in discrete and continuous time, martingale convergence theorems, brownian motion). I have a set of lecture notes I am reading but would appreciate some alte…

My favourite introduction to stochastic processes and stochastic calculus is the book Stochastic Calculus by Paolo Baldi. It is very clear yet precise at the same time, and comes with hundreds of exercises with full solutions prepared. It hits all the important topics - conditional probability, Markov processes, martingale theory, stochastic calculus with respect to Brownian motion, and SDEs. If …

Matrix concentration for Markov chains was initiated in the expander-walk setting by Garg, Lee, Song, and Srivastava'18 [GLSS18]. However, the constant obtained in [GLSS18] is quite loose, and it is natural to ask whether a tighter proof can yield the same constant as in the independent matrix concentration setting. In this paper, we provide a positive answer to this question. Our Hoeffding expon…

The solution to today’s puzzle Earlier today I set you a new twist on the Monty Hall problem, which is (according to AI) the most discussed recreational maths puzzle in history. The standard Monty Hall problem is as follows: Continue reading...

Take this puzzle by the horns Today’s puzzle is a new twist on The Monty Hall problem, arguably the greatest maths puzzle of all time. (According to Gemini, who trawled the internet for me, it is the most discussed and debated recreational maths puzzle of all time.) Continue reading...