This web content provides a basic and intuitive introduction to stochastic calculus, focusing on Brownian motion and its applications in various fields. It avoids complex formalisms and emphasizes physical intuition, discussing the emergence of stochastic calculus from the real world. The author highlights the application of stochastic calculus in modeling stock prices, biology, and physics, with examples like option pricing and random walks. The discussion transitions to Itô calculus, developed to handle the irregular and random nature of Brownian motion, introducing concepts such as the Itô integral and Itô’s Lemma. Notable content includes visualizations of Pascal’s triangle and binomial distributions, along with animations illustrating stochastic processes.
https://jiha-kim.github.io/posts/introduction-to-stochastic-calculus/