The non-Markovian property of q-Gaussian process. (15th March 2020) - Liu, Li-Min; Cui, Ying-Ying; Xu, Jie; Li, Chao; Gao, Qing-Hui
Abstract: In this paper, the q -Gaussian process based on the non-extensive theory is discussed from a mathematical point of view, which has been widely applied to many anomalous diffusion systems in physics and finance. Firstly, the discussion of non-Markovian property of q -Gaussian process provides a numerical support for the future theoretical research. Secondly, the martingale and self-similarity of this process are obtained by Tsallis distributions. Thirdly, the long dependence is analyzed by simulations and Hurst exponents are compared with those of fractional Brownian motion. At last, the European call option price formula driven by this process is simulated, by which we find that this process can better match anomalous diffusion and the volatility smile.