 Brownian moment recursion

For standard one-dimensional Brownian motion, the Itô formula for $B^k$ gives this recursion. Stop at exits from $[-n,n]$ to make the stochastic integral a true martingale. Gaussian tail integrability and the Doob Lp maximal inequality dominate all stopped powers on a fixed horizon, justifying the limit. Odd moments vanish and $\mathbb{E}{B}_t^{2k}=(2k)!t^k/(2^{k}k!)$.

// Target: probability-and-statistics.bigb