The Riccati System and a Diffusion-Type Equation

Mathematics

Erwin Suazo¹  Sergei K. Suslov¹ 

[1] School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287–1804, USA; E-Mail:

关键词: 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;   

DOI  :  10.3390/math2020096

来源: mdpi

【 摘 要 】

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.

【 授权许可】

CC BY   
© 2014 by the authors; licensee MDPI, Basel, Switzerland.