Free CIR processes
- 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 byFor 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.…
| Author: | Holger Graf, Henry Port, Georg Schlüchtermann |
|---|---|
| DOI: | https://doi.org/10.1142/S0219025722500126 |
| ISSN/eISSN: | 0219-0257 |
| Parent Title (English): | Infinite Dimensional Analysis, Quantum Probability and Related Topics |
| Publisher: | World Scientific Pub Co Pte Ltd |
| Document Type: | Article |
| Language: | English |
| Date of Publication (online): | 2022/07/26 |
| Publishing Institution: | Hochschule Nürtingen-Geislingen |
| Release Date: | 2023/08/10 |
| Tag: | Applied Mathematics; Mathematical Physics; Statistical and Nonlinear Physics; Statistics and Probability |
| Volume: | 25 |
| Issue: | 03 |
| Article Number: | 2250012 |
| Institutes: | Fakultät Betriebswirtschaft und Internationale Finanzen |
| open access: | nein |
| Licence (German): |  Urheberrechtlich geschützt |