Lecture

White Noise Form of the Langevin Equation

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Description

This lecture covers the white noise form of the Langevin equation, discussing topics such as the Langevin equation in white noise form, recasting the Fokker-Planck equation, and the Brownian motion. It delves into the mathematical details of stochastic processes and their applications.

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Stochastic differential equation

A stochastic differential equation (SDE) is a differential equation in which one or more of the terms is a stochastic process, resulting in a solution which is also a stochastic process. SDEs have many applications throughout pure mathematics and are used to model various behaviours of stochastic models such as stock prices, random growth models or physical systems that are subjected to thermal fluctuations. SDEs have a random differential that is in the most basic case random white noise calculated as the derivative of a Brownian motion or more generally a semimartingale.

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