Fractional Brownian Motion and Its Increments as Undulatory Models

Fractional Brownian motion (FBM) and its increments are important models in biomedical signal processing, physiology, and traditional Chinese medicine (TCM). They are also used to explain the theory of optics, laser dynamics, and phase transition problems in modern physics. Hence, it is imperative to investigate the essential ideas behind these models. Our analysis indicates that the reason why they can readily account for many of these diverse phenomena in physiology, biomedicine, TCM and physics is that they are intrinsically the random wave theories of continua initiated from complex dynamics. Meanwhile, to illustrate their power, the models are also applied to resolve some paradoxes in quantum mechanics and astronomical phenomena accompanying with the solar spectrum.