Free CIR processes

Graf, Holger; Port, Henry und Schluechtermann, Georg (2022): Free CIR processes. In: Infinite Dimensional Analysis Quantum Probability and Related Topics, Bd. 25, Nr. 3, 2250012

Abstract

For stochastic processes of non-commuting random variables, we formulate a Cox-Ingersoll-Ross (CIR) stochastic differential equation in the context of free probability theory which was introduced by D. Voiculescu. By transforming the classical CIR equation and the Feller condition, which ensures the existence of a positive solution, into the free setting (in the sense of having a strictly positive spectrum), we show the global existence for a free CIR equation. The main challenge lies in the transition from a stochastic differential equation driven by a classical Brownian motion to a stochastic differential equation driven by the free analogue to the classical Brownian motion, the so-called free Brownian motion.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Mathematik, Informatik und Statistik > Statistik
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik
• ISSN: 0219-0257
• Sprache: Englisch