We discuss a method of constructing solutions of the initial value problem for diffusion-type equations in terms of solutions of certain Riccati and Ermakov-type systems. A nonautonomous Burgers-type equation is also considered. Examples include, but are not limited to the Fokker-Planck equation in physics, the Black-Scholes equation and the Hull-White model in finance.
Suazo, E., Suslov, S., & Vega-Guzmán, J. (2014). The Riccati System and a Diffusion-Type Equation. Mathematics, 2(2), 96-118. doi:10.3390/math2020096
- 2017-04-24 11:15:40
- 2021-06-17 05:40:09
- 2 months 4 weeks ago