The Riccati System and a Diffusion-Type Equation

Erwin Suazo, Sergei K. Suslov and José M. Vega-Guzmán
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Erwin Suazo: School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287–1804, USA
Sergei K. Suslov: School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287–1804, USA
José M. Vega-Guzmán: Department of Mathematics, Howard University, 223 Academic Support Building B, Washington,DC 20059, USA

Mathematics, 2014, vol. 2, issue 2, 1-23

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2014
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