Stochastic Calculus and Stochastic Integration
Stochastic Calculus and Stochastic Integration
Stochastic calculus is the branch of mathematics which studies stochastic processes. Anticipated by Louis Bachelier and Albert Einstein at the beginning of the 20th century, the fields of stochastic calculus and stochastic integration were only formalised after the second world war, by Kiyoshi Itô and Norbert Wiener. Stochastic processes are everywhere: the Ornstein–Uhlenbeck process is used in mechanics and evolutionary biology; the Black-Scholes Model is still the gold standard when pricing options. Stochastic processes can even beat state-of-the-art generative models such as GAN. Now that’s a good reason to get a PhD tutor to speed up your learning of stochastic calculus and stochastic analysis!
Among other topics, your stochastics tutor will teach
- Probability distributions, expectations and conditional expectations
- Riemann–Stieltjes integration, Itô integration and Stratonovich integration
- Brownian motion, Lévy processes and semimartingale theory
- Stochastic differential equations, such as the Ornstein–Uhlenbeck process
- Stochastic filtering, including the Kalman-Bucy filter and the innovation process
Regardless of whether you’re starting from scratch or have studied stochastic calculus or stochastic integration before, your tutor will adapt to your level and explain complex concepts in simple terms. The tutor will first equip the students with the necessary knowledge of Itô Calculus, Stochastic Integration by parts, Montecarlo methods, etc. and then directly apply the acquired knowledge and skills to real-life problems which arise in the industry. What kind of real-life problems? Check this out! NASA used stochastic filtering to send the Apollo missions to the moon.