Applying the theory of voter model and the theory of stopping time, we investigate the statistical properties of the fluctuations of interfaces model that defined from the voter model. We show that the probability distributions of the fluctuations, under some conditions, converge to the corresponding distribution of a geometric Brownian motion. Key-Words: Fluctuation; interface; voter model; st...

In this paper, we continue the study of the geometry of Brownian motions which are encoded by Kolmogorov-Chaitin random reals (complex oscillations). We unfold Kolmogorov-Chaitin complexity in the context of Brownian motion and specifically to phenomena emerging from the random geometric patterns generated by a Brownian motion.

A geometric Brownian motion with delay is the solution of a stochastic differential equation where the drift and diffusion coefficient depend linearly on the past of the solution, i.e. a linear stochastic functional differential equation. In this work the asymptotic behavior in mean square of a geometric Brownian motion with delay is completely characterized by a sufficient and necessary condit...

Asset prices are typically modeled with the geometric Brownian motion (GBM). Correlation between the assets is exogenously modeled and then ad-hoc assigned to the asset prices. This is conceptually and mathematically unsatisfying. We create a new, simple approach, which simultaneously models stochastic volatility and stochastic correlation. This approach replicates the realworld volatility – co...