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What is Itô Calculus and Stochastic Integrals about?
The document discusses Itô integrals and calculus. It begins by motivating Itô integrals through diffusion processes and Brownian motion. It then proves that Brownian motion paths are nowhere differentiable, preventing the use of traditional calculus. The construction of the Itô integral is then introduced for simple functions over partitions of time intervals. Key properties of the Itô integral are presented, including that it has an expected value of 0 and satisfies the Itô isometry.
- Language
- EN