Welcome — and a note on Brownian motion

This is the first post on this site — and a demonstration that writing here is just Markdown with full LaTeX support.

Math works out of the box

Inline math like WtN(0,t)W_t \sim \mathcal{N}(0, t) renders inline, and display math gets its own block:

dXt=μ(Xt)dt+σ(Xt)dWtdX_t = \mu(X_t)\,dt + \sigma(X_t)\,dW_t

The quadratic variation of standard Brownian motion satisfies Wt=t\langle W \rangle_t = t, which is the reason Itô calculus needs its correction term:

df(Xt)=f(Xt)dXt+12f(Xt)dXt.df(X_t) = f'(X_t)\,dX_t + \tfrac{1}{2} f''(X_t)\,d\langle X \rangle_t .

How to write a new post

Create a new .md file in content/posts/, give it a title and a date in the frontmatter, push to main — the site rebuilds and deploys itself.