Stochastic Calculus
Brownian Motion for Dummies
The same random walk with finer and finer steps: a path that is everywhere continuous and nowhere smooth.
What to remember
- W_t ~ N(0, t): independent Gaussian increments with variance equal to elapsed time.
- Spread grows like √t.
- Reflection: P(max ≥ a) = 2 P(W_T ≥ a).
Read the lessonBrownian Motion, with a checkpoint at the end.