The Riccati system and a diffusion-type equation

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

Research output: Contribution to journalArticle

8 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 languageEnglish (US)
Pages (from-to)96-118
Number of pages23
JournalMathematics
Volume2
Issue number2
DOIs
StatePublished - 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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