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.
- The Riccati System and a Diffusion-Type Equation
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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