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.