Martingale Marginals

[This post originates from twitter threads posted on 9 Sep 21 and 2 Feb 22.]

A while ago, I proved the result: A continuous strong Markov martingale is uniquely determined by its marginal distributions. This is discussed in a recent paper by Beiglböck, Pammer, and Schachermayer.

Time for a thread discussing some of these ideas, which have been studied for decades in both stochastic calculus and mathematical finance. Continue reading “Martingale Marginals”

The Collatz Conjecture

[This post originates from a twitter thread on the Collatz conjecture.]

Time for some #RandomNumberTheory. The Collatz Conjecture is a famous unsolved mathematical problem which also goes by various other names, such as the ‘3n+1’ conjecture. Since it was introduced by Lothar Collatz in 1937, no-one has been able to prove it either true or false.

I dont know

I dont know

Continue reading “The Collatz Conjecture”