Mathematics 2014, 2(2), 96-118; doi:10.3390/math2020096
Article

The Riccati System and a Diffusion-Type Equation

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Received: 31 December 2013; in revised form: 27 February 2014 / Accepted: 14 April 2014 / Published: 15 May 2014
(This article belongs to the Special Issue Mathematics on Partial Differential Equations)
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Abstract: 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.
Keywords: diffusion-type equations; Green’s function; fundamental solution; autonomous and nonautonomous Burgers equations; Fokker-Planck equation; Black-Scholes equation; the Hull-White model; Riccati equation and Riccati-type system; Ermakov equation and Ermakov-type system
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MDPI and ACS Style

Suazo, E.; Suslov, S.K.; Vega-Guzmán, J.M. The Riccati System and a Diffusion-Type Equation. Mathematics 2014, 2, 96-118.

AMA Style

Suazo E, Suslov SK, Vega-Guzmán JM. The Riccati System and a Diffusion-Type Equation. Mathematics. 2014; 2(2):96-118.

Chicago/Turabian Style

Suazo, Erwin; Suslov, Sergei K.; Vega-Guzmán, José M. 2014. "The Riccati System and a Diffusion-Type Equation." Mathematics 2, no. 2: 96-118.

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