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FokkerPlanckEquation
The Fokker-Planck equation, also known as the Kolmogorov forward equation, is a partial differential equation that describes the time evolution of the probability density function of a stochastic process. It is widely used in various fields, such as statistical physics, financial mathematics, and population biology.
The general form of the Fokker-Planck equation is given by:
where
The Fokker-Planck equation can be used to model a wide range of stochastic processes, including Brownian motion, which describes the random motion of particles suspended in a fluid.
There are many techniques available for solving the Fokker-Planck equation, including numerical methods and analytical techniques such as perturbation theory and the method of characteristics. These methods can be used to study the properties of stochastic systems, such as the probability of a particle reaching a certain position or the time it takes for a particle to diffuse a certain distance.
Overall, the Fokker-Planck equation provides a powerful tool for understanding the behavior of stochastic systems, and has numerous applications in physics, chemistry, biology, and finance.