The Riccati System and a Diffusion-Type Equation

  title={The Riccati System and a Diffusion-Type Equation},
  author={E. Suazo and Sergei K. Suslov and Jos{\'e} M. Vega-Guzm{\'a}n},
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. 

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