Sub-fractional G-Brownian motion: Properties and simulations
In this article, we introduce a new stochastic process called the sub-fractional G-Brownian motion, which serves as an intermediate between the G-Brownian motion and the fractional G-Brownian motion. Although the sub-fractional G-Brownian motion shares some properties with the fractional G-Brownian motion, it features nonstationary increments. We then examine key characteristics of the process, such as self-similarity, H\"{o}lder continuity, and long-range dependence. Additionally, we propose a method for simulating sample paths of sub-fractional G-Brownian motion and conclude by simulating linear stochastic differential equations driven by sub-fractional G-Brownian motion.
We focus on solving stochastic differential equations driven by jump processes (SDEJs) with measurable drifts that may exhibit quadratic growth. Our approach leverages
In this short note we provide an additional term that was missing in the proof of Theorem 5.1 in section 5 (Comparison and strict comparison theorems) of our previous paper entitled: Quadratic…
In this article, we introduce a new stochastic process called the sub-fractional G-Brownian motion, which serves as an intermediate between the G-Brownian motion and the fractional G-Brownian…