The Riccati system and a diffusion-type equation

Erwin Suazo; Sergei Suslov; José M. Vega-Guzmán

doi:10.3390/math2020096

The Riccati system and a diffusion-type equation

Erwin Suazo, Sergei Suslov, José M. Vega-Guzmán

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

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.

Original language	English (US)
Pages (from-to)	96-118
Number of pages	23
Journal	Mathematics
Volume	2
Issue number	2
DOIs	https://doi.org/10.3390/math2020096
State	Published - Jun 1 2014

Keywords

Autonomous and nonautonomous Burgers equations
Black-Scholes equation
Diffusion-type equations
Ermakov equation and Ermakov-type system
Fokker-Planck equation
Fundamental solution
Green's function
Riccati equation and Riccati-type system
The Hull-White model

ASJC Scopus subject areas

Mathematics(all)

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10.3390/math2020096

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title = "The Riccati system and a diffusion-type equation",

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 = "Autonomous and nonautonomous Burgers equations, Black-Scholes equation, Diffusion-type equations, Ermakov equation and Ermakov-type system, Fokker-Planck equation, Fundamental solution, Green's function, Riccati equation and Riccati-type system, The Hull-White model",

author = "Erwin Suazo and Sergei Suslov and Vega-Guzm{\'a}n, {Jos{\'e} M.}",

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T1 - The Riccati system and a diffusion-type equation

AU - Suazo, Erwin

AU - Suslov, Sergei

AU - Vega-Guzmán, José M.

PY - 2014/6/1

Y1 - 2014/6/1

N2 - 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.

AB - 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.

KW - Autonomous and nonautonomous Burgers equations

KW - Black-Scholes equation

KW - Diffusion-type equations

KW - Ermakov equation and Ermakov-type system

KW - Fokker-Planck equation

KW - Fundamental solution

KW - Green's function

KW - Riccati equation and Riccati-type system

KW - The Hull-White model

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The Riccati system and a diffusion-type equation

Abstract

Keywords

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