Itô stochastic calculus
Cálculo estocástico de Itô
- Date
- 1944 · confidence high
- Place
- Tokyo, Japan
- Credited to
- Kiyosi Itô; Wiener's Brownian motion (1923)
- People
- 👤 Kiyoshi Itō1915–2008
- Field
- Knowledge & symbols
What was discovered
An integral with respect to Brownian motion and Itô's formula (the chain rule for random processes), which makes it possible to set up stochastic differential equations. The basis of financial mathematics and signal filtering.
Published in Japanese during the war, it took years to become known in the West.
What it led to
- stochastic differential equations
- the Black-Scholes model
- the Kalman-Bucy filter
- statistical physics
Built on
- Kolmogorov axioms
- Wiener process
- Bachelier (1900)
Made possible
- Ship's inertial navigation system (SINS)1958
- Black-Scholes-Merton equation1973
- valuation of financial derivatives