An interactive learning path from random walks to financial applications.
From the discrete random walk to continuous Brownian motion.
Defining the Wiener process, its increments and covariance.
Running maximum, the reflection principle and first passage times.
Stochastic integration, the Itô isometry and Itô's lemma.
Structured lessons planned; the standalone lab is available meanwhile.
Arithmetic and geometric Brownian motion, Euler–Maruyama, mean reversion.
Structured lessons planned; the standalone lab is available meanwhile.
Martingales, stopping times, filtrations and Girsanov's theorem.
This chapter is still in development.
A general-purpose simulation laboratory and financial applications.
Structured lessons planned; the standalone lab is available meanwhile.
A hands-on course in stochastic processes and stochastic calculus. Each lesson poses a question and lets you answer it by experiment: from the symmetric random walk and the √t scaling law, through the central limit theorem and Donsker's theorem, to the Wiener process, its increments and covariance, the running maximum, the reflection principle and first passage times.
No. The lessons start from coin flips and build up step by step; each one has an Explore tab with experiments and a Mathematics tab with the precise statements.
Its increments over disjoint intervals are independent, so their variances add. Variance therefore grows linearly in time and the typical deviation, the standard deviation, grows like √t.